1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
77 <option>-fglasgow-exts</option>:
78 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
81 <para>This simultaneously enables all of the extensions to
82 Haskell 98 described in <xref
83 linkend="ghc-language-features"/>, except where otherwise
86 <para>New reserved words: <literal>forall</literal> (only in
87 types), <literal>mdo</literal>.</para>
89 <para>Other syntax stolen:
90 <replaceable>varid</replaceable>{<literal>#</literal>},
91 <replaceable>char</replaceable><literal>#</literal>,
92 <replaceable>string</replaceable><literal>#</literal>,
93 <replaceable>integer</replaceable><literal>#</literal>,
94 <replaceable>float</replaceable><literal>#</literal>,
95 <replaceable>float</replaceable><literal>##</literal>,
96 <literal>(#</literal>, <literal>#)</literal>,
97 <literal>|)</literal>, <literal>{|</literal>.</para>
103 <option>-ffi</option> and <option>-fffi</option>:
104 <indexterm><primary><option>-ffi</option></primary></indexterm>
105 <indexterm><primary><option>-fffi</option></primary></indexterm>
108 <para>This option enables the language extension defined in the
109 Haskell 98 Foreign Function Interface Addendum plus deprecated
110 syntax of previous versions of the FFI for backwards
111 compatibility.</para>
113 <para>New reserved words: <literal>foreign</literal>.</para>
119 <option>-fno-monomorphism-restriction</option>:
120 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
123 <para> Switch off the Haskell 98 monomorphism restriction.
124 Independent of the <option>-fglasgow-exts</option>
131 <option>-fallow-overlapping-instances</option>
132 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
135 <option>-fallow-undecidable-instances</option>
136 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
139 <option>-fallow-incoherent-instances</option>
140 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
143 <option>-fcontext-stack=N</option>
144 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
147 <para> See <xref linkend="instance-decls"/>. Only relevant
148 if you also use <option>-fglasgow-exts</option>.</para>
154 <option>-finline-phase</option>
155 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
158 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
159 you also use <option>-fglasgow-exts</option>.</para>
165 <option>-farrows</option>
166 <indexterm><primary><option>-farrows</option></primary></indexterm>
169 <para>See <xref linkend="arrow-notation"/>. Independent of
170 <option>-fglasgow-exts</option>.</para>
172 <para>New reserved words/symbols: <literal>rec</literal>,
173 <literal>proc</literal>, <literal>-<</literal>,
174 <literal>>-</literal>, <literal>-<<</literal>,
175 <literal>>>-</literal>.</para>
177 <para>Other syntax stolen: <literal>(|</literal>,
178 <literal>|)</literal>.</para>
184 <option>-fgenerics</option>
185 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
188 <para>See <xref linkend="generic-classes"/>. Independent of
189 <option>-fglasgow-exts</option>.</para>
194 <term><option>-fno-implicit-prelude</option></term>
196 <para><indexterm><primary>-fno-implicit-prelude
197 option</primary></indexterm> GHC normally imports
198 <filename>Prelude.hi</filename> files for you. If you'd
199 rather it didn't, then give it a
200 <option>-fno-implicit-prelude</option> option. The idea is
201 that you can then import a Prelude of your own. (But don't
202 call it <literal>Prelude</literal>; the Haskell module
203 namespace is flat, and you must not conflict with any
204 Prelude module.)</para>
206 <para>Even though you have not imported the Prelude, most of
207 the built-in syntax still refers to the built-in Haskell
208 Prelude types and values, as specified by the Haskell
209 Report. For example, the type <literal>[Int]</literal>
210 still means <literal>Prelude.[] Int</literal>; tuples
211 continue to refer to the standard Prelude tuples; the
212 translation for list comprehensions continues to use
213 <literal>Prelude.map</literal> etc.</para>
215 <para>However, <option>-fno-implicit-prelude</option> does
216 change the handling of certain built-in syntax: see <xref
217 linkend="rebindable-syntax"/>.</para>
222 <term><option>-fimplicit-params</option></term>
224 <para>Enables implicit parameters (see <xref
225 linkend="implicit-parameters"/>). Currently also implied by
226 <option>-fglasgow-exts</option>.</para>
229 <literal>?<replaceable>varid</replaceable></literal>,
230 <literal>%<replaceable>varid</replaceable></literal>.</para>
235 <term><option>-fscoped-type-variables</option></term>
237 <para>Enables lexically-scoped type variables (see <xref
238 linkend="scoped-type-variables"/>). Implied by
239 <option>-fglasgow-exts</option>.</para>
244 <term><option>-fth</option></term>
246 <para>Enables Template Haskell (see <xref
247 linkend="template-haskell"/>). This flag must
248 be given explicitly; it is no longer implied by
249 <option>-fglasgow-exts</option>.</para>
251 <para>Syntax stolen: <literal>[|</literal>,
252 <literal>[e|</literal>, <literal>[p|</literal>,
253 <literal>[d|</literal>, <literal>[t|</literal>,
254 <literal>$(</literal>,
255 <literal>$<replaceable>varid</replaceable></literal>.</para>
262 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
263 <!-- included from primitives.sgml -->
264 <!-- &primitives; -->
265 <sect1 id="primitives">
266 <title>Unboxed types and primitive operations</title>
268 <para>GHC is built on a raft of primitive data types and operations.
269 While you really can use this stuff to write fast code,
270 we generally find it a lot less painful, and more satisfying in the
271 long run, to use higher-level language features and libraries. With
272 any luck, the code you write will be optimised to the efficient
273 unboxed version in any case. And if it isn't, we'd like to know
276 <para>We do not currently have good, up-to-date documentation about the
277 primitives, perhaps because they are mainly intended for internal use.
278 There used to be a long section about them here in the User Guide, but it
279 became out of date, and wrong information is worse than none.</para>
281 <para>The Real Truth about what primitive types there are, and what operations
282 work over those types, is held in the file
283 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
284 This file is used directly to generate GHC's primitive-operation definitions, so
285 it is always correct! It is also intended for processing into text.</para>
288 the result of such processing is part of the description of the
290 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
291 Core language</ulink>.
292 So that document is a good place to look for a type-set version.
293 We would be very happy if someone wanted to volunteer to produce an SGML
294 back end to the program that processes <filename>primops.txt</filename> so that
295 we could include the results here in the User Guide.</para>
297 <para>What follows here is a brief summary of some main points.</para>
299 <sect2 id="glasgow-unboxed">
304 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
307 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
308 that values of that type are represented by a pointer to a heap
309 object. The representation of a Haskell <literal>Int</literal>, for
310 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
311 type, however, is represented by the value itself, no pointers or heap
312 allocation are involved.
316 Unboxed types correspond to the “raw machine” types you
317 would use in C: <literal>Int#</literal> (long int),
318 <literal>Double#</literal> (double), <literal>Addr#</literal>
319 (void *), etc. The <emphasis>primitive operations</emphasis>
320 (PrimOps) on these types are what you might expect; e.g.,
321 <literal>(+#)</literal> is addition on
322 <literal>Int#</literal>s, and is the machine-addition that we all
323 know and love—usually one instruction.
327 Primitive (unboxed) types cannot be defined in Haskell, and are
328 therefore built into the language and compiler. Primitive types are
329 always unlifted; that is, a value of a primitive type cannot be
330 bottom. We use the convention that primitive types, values, and
331 operations have a <literal>#</literal> suffix.
335 Primitive values are often represented by a simple bit-pattern, such
336 as <literal>Int#</literal>, <literal>Float#</literal>,
337 <literal>Double#</literal>. But this is not necessarily the case:
338 a primitive value might be represented by a pointer to a
339 heap-allocated object. Examples include
340 <literal>Array#</literal>, the type of primitive arrays. A
341 primitive array is heap-allocated because it is too big a value to fit
342 in a register, and would be too expensive to copy around; in a sense,
343 it is accidental that it is represented by a pointer. If a pointer
344 represents a primitive value, then it really does point to that value:
345 no unevaluated thunks, no indirections…nothing can be at the
346 other end of the pointer than the primitive value.
347 A numerically-intensive program using unboxed types can
348 go a <emphasis>lot</emphasis> faster than its “standard”
349 counterpart—we saw a threefold speedup on one example.
353 There are some restrictions on the use of primitive types:
355 <listitem><para>The main restriction
356 is that you can't pass a primitive value to a polymorphic
357 function or store one in a polymorphic data type. This rules out
358 things like <literal>[Int#]</literal> (i.e. lists of primitive
359 integers). The reason for this restriction is that polymorphic
360 arguments and constructor fields are assumed to be pointers: if an
361 unboxed integer is stored in one of these, the garbage collector would
362 attempt to follow it, leading to unpredictable space leaks. Or a
363 <function>seq</function> operation on the polymorphic component may
364 attempt to dereference the pointer, with disastrous results. Even
365 worse, the unboxed value might be larger than a pointer
366 (<literal>Double#</literal> for instance).
369 <listitem><para> You cannot bind a variable with an unboxed type
370 in a <emphasis>top-level</emphasis> binding.
372 <listitem><para> You cannot bind a variable with an unboxed type
373 in a <emphasis>recursive</emphasis> binding.
375 <listitem><para> You may bind unboxed variables in a (non-recursive,
376 non-top-level) pattern binding, but any such variable causes the entire
378 to become strict. For example:
380 data Foo = Foo Int Int#
382 f x = let (Foo a b, w) = ..rhs.. in ..body..
384 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
386 is strict, and the program behaves as if you had written
388 data Foo = Foo Int Int#
390 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
399 <sect2 id="unboxed-tuples">
400 <title>Unboxed Tuples
404 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
405 they're available by default with <option>-fglasgow-exts</option>. An
406 unboxed tuple looks like this:
418 where <literal>e_1..e_n</literal> are expressions of any
419 type (primitive or non-primitive). The type of an unboxed tuple looks
424 Unboxed tuples are used for functions that need to return multiple
425 values, but they avoid the heap allocation normally associated with
426 using fully-fledged tuples. When an unboxed tuple is returned, the
427 components are put directly into registers or on the stack; the
428 unboxed tuple itself does not have a composite representation. Many
429 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
431 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
432 tuples to avoid unnecessary allocation during sequences of operations.
436 There are some pretty stringent restrictions on the use of unboxed tuples:
441 Values of unboxed tuple types are subject to the same restrictions as
442 other unboxed types; i.e. they may not be stored in polymorphic data
443 structures or passed to polymorphic functions.
450 No variable can have an unboxed tuple type, nor may a constructor or function
451 argument have an unboxed tuple type. The following are all illegal:
455 data Foo = Foo (# Int, Int #)
457 f :: (# Int, Int #) -> (# Int, Int #)
460 g :: (# Int, Int #) -> Int
463 h x = let y = (# x,x #) in ...
470 The typical use of unboxed tuples is simply to return multiple values,
471 binding those multiple results with a <literal>case</literal> expression, thus:
473 f x y = (# x+1, y-1 #)
474 g x = case f x x of { (# a, b #) -> a + b }
476 You can have an unboxed tuple in a pattern binding, thus
478 f x = let (# p,q #) = h x in ..body..
480 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
481 the resulting binding is lazy like any other Haskell pattern binding. The
482 above example desugars like this:
484 f x = let t = case h x o f{ (# p,q #) -> (p,q)
489 Indeed, the bindings can even be recursive.
496 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
498 <sect1 id="syntax-extns">
499 <title>Syntactic extensions</title>
501 <!-- ====================== HIERARCHICAL MODULES ======================= -->
503 <sect2 id="hierarchical-modules">
504 <title>Hierarchical Modules</title>
506 <para>GHC supports a small extension to the syntax of module
507 names: a module name is allowed to contain a dot
508 <literal>‘.’</literal>. This is also known as the
509 “hierarchical module namespace” extension, because
510 it extends the normally flat Haskell module namespace into a
511 more flexible hierarchy of modules.</para>
513 <para>This extension has very little impact on the language
514 itself; modules names are <emphasis>always</emphasis> fully
515 qualified, so you can just think of the fully qualified module
516 name as <quote>the module name</quote>. In particular, this
517 means that the full module name must be given after the
518 <literal>module</literal> keyword at the beginning of the
519 module; for example, the module <literal>A.B.C</literal> must
522 <programlisting>module A.B.C</programlisting>
525 <para>It is a common strategy to use the <literal>as</literal>
526 keyword to save some typing when using qualified names with
527 hierarchical modules. For example:</para>
530 import qualified Control.Monad.ST.Strict as ST
533 <para>For details on how GHC searches for source and interface
534 files in the presence of hierarchical modules, see <xref
535 linkend="search-path"/>.</para>
537 <para>GHC comes with a large collection of libraries arranged
538 hierarchically; see the accompanying library documentation.
539 There is an ongoing project to create and maintain a stable set
540 of <quote>core</quote> libraries used by several Haskell
541 compilers, and the libraries that GHC comes with represent the
542 current status of that project. For more details, see <ulink
543 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
544 Libraries</ulink>.</para>
548 <!-- ====================== PATTERN GUARDS ======================= -->
550 <sect2 id="pattern-guards">
551 <title>Pattern guards</title>
554 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
555 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
559 Suppose we have an abstract data type of finite maps, with a
563 lookup :: FiniteMap -> Int -> Maybe Int
566 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
567 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
571 clunky env var1 var2 | ok1 && ok2 = val1 + val2
572 | otherwise = var1 + var2
583 The auxiliary functions are
587 maybeToBool :: Maybe a -> Bool
588 maybeToBool (Just x) = True
589 maybeToBool Nothing = False
591 expectJust :: Maybe a -> a
592 expectJust (Just x) = x
593 expectJust Nothing = error "Unexpected Nothing"
597 What is <function>clunky</function> doing? The guard <literal>ok1 &&
598 ok2</literal> checks that both lookups succeed, using
599 <function>maybeToBool</function> to convert the <function>Maybe</function>
600 types to booleans. The (lazily evaluated) <function>expectJust</function>
601 calls extract the values from the results of the lookups, and binds the
602 returned values to <varname>val1</varname> and <varname>val2</varname>
603 respectively. If either lookup fails, then clunky takes the
604 <literal>otherwise</literal> case and returns the sum of its arguments.
608 This is certainly legal Haskell, but it is a tremendously verbose and
609 un-obvious way to achieve the desired effect. Arguably, a more direct way
610 to write clunky would be to use case expressions:
614 clunky env var1 var1 = case lookup env var1 of
616 Just val1 -> case lookup env var2 of
618 Just val2 -> val1 + val2
624 This is a bit shorter, but hardly better. Of course, we can rewrite any set
625 of pattern-matching, guarded equations as case expressions; that is
626 precisely what the compiler does when compiling equations! The reason that
627 Haskell provides guarded equations is because they allow us to write down
628 the cases we want to consider, one at a time, independently of each other.
629 This structure is hidden in the case version. Two of the right-hand sides
630 are really the same (<function>fail</function>), and the whole expression
631 tends to become more and more indented.
635 Here is how I would write clunky:
640 | Just val1 <- lookup env var1
641 , Just val2 <- lookup env var2
643 ...other equations for clunky...
647 The semantics should be clear enough. The qualifiers are matched in order.
648 For a <literal><-</literal> qualifier, which I call a pattern guard, the
649 right hand side is evaluated and matched against the pattern on the left.
650 If the match fails then the whole guard fails and the next equation is
651 tried. If it succeeds, then the appropriate binding takes place, and the
652 next qualifier is matched, in the augmented environment. Unlike list
653 comprehensions, however, the type of the expression to the right of the
654 <literal><-</literal> is the same as the type of the pattern to its
655 left. The bindings introduced by pattern guards scope over all the
656 remaining guard qualifiers, and over the right hand side of the equation.
660 Just as with list comprehensions, boolean expressions can be freely mixed
661 with among the pattern guards. For example:
672 Haskell's current guards therefore emerge as a special case, in which the
673 qualifier list has just one element, a boolean expression.
677 <!-- ===================== Recursive do-notation =================== -->
679 <sect2 id="mdo-notation">
680 <title>The recursive do-notation
683 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
684 "A recursive do for Haskell",
685 Levent Erkok, John Launchbury",
686 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
689 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
690 that is, the variables bound in a do-expression are visible only in the textually following
691 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
692 group. It turns out that several applications can benefit from recursive bindings in
693 the do-notation, and this extension provides the necessary syntactic support.
696 Here is a simple (yet contrived) example:
699 import Control.Monad.Fix
701 justOnes = mdo xs <- Just (1:xs)
705 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
709 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
712 class Monad m => MonadFix m where
713 mfix :: (a -> m a) -> m a
716 The function <literal>mfix</literal>
717 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
718 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
719 For details, see the above mentioned reference.
722 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
723 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
724 for Haskell's internal state monad (strict and lazy, respectively).
727 There are three important points in using the recursive-do notation:
730 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
731 than <literal>do</literal>).
735 You should <literal>import Control.Monad.Fix</literal>.
736 (Note: Strictly speaking, this import is required only when you need to refer to the name
737 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
738 are encouraged to always import this module when using the mdo-notation.)
742 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
748 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
749 contains up to date information on recursive monadic bindings.
753 Historical note: The old implementation of the mdo-notation (and most
754 of the existing documents) used the name
755 <literal>MonadRec</literal> for the class and the corresponding library.
756 This name is not supported by GHC.
762 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
764 <sect2 id="parallel-list-comprehensions">
765 <title>Parallel List Comprehensions</title>
766 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
768 <indexterm><primary>parallel list comprehensions</primary>
771 <para>Parallel list comprehensions are a natural extension to list
772 comprehensions. List comprehensions can be thought of as a nice
773 syntax for writing maps and filters. Parallel comprehensions
774 extend this to include the zipWith family.</para>
776 <para>A parallel list comprehension has multiple independent
777 branches of qualifier lists, each separated by a `|' symbol. For
778 example, the following zips together two lists:</para>
781 [ (x, y) | x <- xs | y <- ys ]
784 <para>The behavior of parallel list comprehensions follows that of
785 zip, in that the resulting list will have the same length as the
786 shortest branch.</para>
788 <para>We can define parallel list comprehensions by translation to
789 regular comprehensions. Here's the basic idea:</para>
791 <para>Given a parallel comprehension of the form: </para>
794 [ e | p1 <- e11, p2 <- e12, ...
795 | q1 <- e21, q2 <- e22, ...
800 <para>This will be translated to: </para>
803 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
804 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
809 <para>where `zipN' is the appropriate zip for the given number of
814 <sect2 id="rebindable-syntax">
815 <title>Rebindable syntax</title>
818 <para>GHC allows most kinds of built-in syntax to be rebound by
819 the user, to facilitate replacing the <literal>Prelude</literal>
820 with a home-grown version, for example.</para>
822 <para>You may want to define your own numeric class
823 hierarchy. It completely defeats that purpose if the
824 literal "1" means "<literal>Prelude.fromInteger
825 1</literal>", which is what the Haskell Report specifies.
826 So the <option>-fno-implicit-prelude</option> flag causes
827 the following pieces of built-in syntax to refer to
828 <emphasis>whatever is in scope</emphasis>, not the Prelude
833 <para>An integer literal <literal>368</literal> means
834 "<literal>fromInteger (368::Integer)</literal>", rather than
835 "<literal>Prelude.fromInteger (368::Integer)</literal>".
838 <listitem><para>Fractional literals are handed in just the same way,
839 except that the translation is
840 <literal>fromRational (3.68::Rational)</literal>.
843 <listitem><para>The equality test in an overloaded numeric pattern
844 uses whatever <literal>(==)</literal> is in scope.
847 <listitem><para>The subtraction operation, and the
848 greater-than-or-equal test, in <literal>n+k</literal> patterns
849 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
853 <para>Negation (e.g. "<literal>- (f x)</literal>")
854 means "<literal>negate (f x)</literal>", both in numeric
855 patterns, and expressions.
859 <para>"Do" notation is translated using whatever
860 functions <literal>(>>=)</literal>,
861 <literal>(>>)</literal>, and <literal>fail</literal>,
862 are in scope (not the Prelude
863 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
864 comprehensions, are unaffected. </para></listitem>
868 notation (see <xref linkend="arrow-notation"/>)
869 uses whatever <literal>arr</literal>,
870 <literal>(>>>)</literal>, <literal>first</literal>,
871 <literal>app</literal>, <literal>(|||)</literal> and
872 <literal>loop</literal> functions are in scope. But unlike the
873 other constructs, the types of these functions must match the
874 Prelude types very closely. Details are in flux; if you want
878 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
879 even if that is a little unexpected. For emample, the
880 static semantics of the literal <literal>368</literal>
881 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
882 <literal>fromInteger</literal> to have any of the types:
884 fromInteger :: Integer -> Integer
885 fromInteger :: forall a. Foo a => Integer -> a
886 fromInteger :: Num a => a -> Integer
887 fromInteger :: Integer -> Bool -> Bool
891 <para>Be warned: this is an experimental facility, with
892 fewer checks than usual. Use <literal>-dcore-lint</literal>
893 to typecheck the desugared program. If Core Lint is happy
894 you should be all right.</para>
900 <!-- TYPE SYSTEM EXTENSIONS -->
901 <sect1 id="type-extensions">
902 <title>Type system extensions</title>
906 <title>Data types and type synonyms</title>
908 <sect3 id="nullary-types">
909 <title>Data types with no constructors</title>
911 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
912 a data type with no constructors. For example:</para>
916 data T a -- T :: * -> *
919 <para>Syntactically, the declaration lacks the "= constrs" part. The
920 type can be parameterised over types of any kind, but if the kind is
921 not <literal>*</literal> then an explicit kind annotation must be used
922 (see <xref linkend="sec-kinding"/>).</para>
924 <para>Such data types have only one value, namely bottom.
925 Nevertheless, they can be useful when defining "phantom types".</para>
928 <sect3 id="infix-tycons">
929 <title>Infix type constructors, classes, and type variables</title>
932 GHC allows type constructors, classes, and type variables to be operators, and
933 to be written infix, very much like expressions. More specifically:
936 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
937 The lexical syntax is the same as that for data constructors.
940 Data type and type-synonym declarations can be written infix, parenthesised
941 if you want further arguments. E.g.
943 data a :*: b = Foo a b
944 type a :+: b = Either a b
945 class a :=: b where ...
947 data (a :**: b) x = Baz a b x
948 type (a :++: b) y = Either (a,b) y
952 Types, and class constraints, can be written infix. For example
955 f :: (a :=: b) => a -> b
959 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
960 The lexical syntax is the same as that for variable operators, excluding "(.)",
961 "(!)", and "(*)". In a binding position, the operator must be
962 parenthesised. For example:
964 type T (+) = Int + Int
969 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
975 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
976 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
979 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
980 one cannot distinguish between the two in a fixity declaration; a fixity declaration
981 sets the fixity for a data constructor and the corresponding type constructor. For example:
985 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
986 and similarly for <literal>:*:</literal>.
987 <literal>Int `a` Bool</literal>.
990 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
997 <sect3 id="type-synonyms">
998 <title>Liberalised type synonyms</title>
1001 Type synonyms are like macros at the type level, and
1002 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1003 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1005 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1006 in a type synonym, thus:
1008 type Discard a = forall b. Show b => a -> b -> (a, String)
1013 g :: Discard Int -> (Int,String) -- A rank-2 type
1020 You can write an unboxed tuple in a type synonym:
1022 type Pr = (# Int, Int #)
1030 You can apply a type synonym to a forall type:
1032 type Foo a = a -> a -> Bool
1034 f :: Foo (forall b. b->b)
1036 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1038 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1043 You can apply a type synonym to a partially applied type synonym:
1045 type Generic i o = forall x. i x -> o x
1048 foo :: Generic Id []
1050 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1052 foo :: forall x. x -> [x]
1060 GHC currently does kind checking before expanding synonyms (though even that
1064 After expanding type synonyms, GHC does validity checking on types, looking for
1065 the following mal-formedness which isn't detected simply by kind checking:
1068 Type constructor applied to a type involving for-alls.
1071 Unboxed tuple on left of an arrow.
1074 Partially-applied type synonym.
1078 this will be rejected:
1080 type Pr = (# Int, Int #)
1085 because GHC does not allow unboxed tuples on the left of a function arrow.
1090 <sect3 id="existential-quantification">
1091 <title>Existentially quantified data constructors
1095 The idea of using existential quantification in data type declarations
1096 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1097 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1098 London, 1991). It was later formalised by Laufer and Odersky
1099 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1100 TOPLAS, 16(5), pp1411-1430, 1994).
1101 It's been in Lennart
1102 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1103 proved very useful. Here's the idea. Consider the declaration:
1109 data Foo = forall a. MkFoo a (a -> Bool)
1116 The data type <literal>Foo</literal> has two constructors with types:
1122 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1129 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1130 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1131 For example, the following expression is fine:
1137 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1143 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1144 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1145 isUpper</function> packages a character with a compatible function. These
1146 two things are each of type <literal>Foo</literal> and can be put in a list.
1150 What can we do with a value of type <literal>Foo</literal>?. In particular,
1151 what happens when we pattern-match on <function>MkFoo</function>?
1157 f (MkFoo val fn) = ???
1163 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1164 are compatible, the only (useful) thing we can do with them is to
1165 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1172 f (MkFoo val fn) = fn val
1178 What this allows us to do is to package heterogenous values
1179 together with a bunch of functions that manipulate them, and then treat
1180 that collection of packages in a uniform manner. You can express
1181 quite a bit of object-oriented-like programming this way.
1184 <sect4 id="existential">
1185 <title>Why existential?
1189 What has this to do with <emphasis>existential</emphasis> quantification?
1190 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1196 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1202 But Haskell programmers can safely think of the ordinary
1203 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1204 adding a new existential quantification construct.
1210 <title>Type classes</title>
1213 An easy extension is to allow
1214 arbitrary contexts before the constructor. For example:
1220 data Baz = forall a. Eq a => Baz1 a a
1221 | forall b. Show b => Baz2 b (b -> b)
1227 The two constructors have the types you'd expect:
1233 Baz1 :: forall a. Eq a => a -> a -> Baz
1234 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1240 But when pattern matching on <function>Baz1</function> the matched values can be compared
1241 for equality, and when pattern matching on <function>Baz2</function> the first matched
1242 value can be converted to a string (as well as applying the function to it).
1243 So this program is legal:
1250 f (Baz1 p q) | p == q = "Yes"
1252 f (Baz2 v fn) = show (fn v)
1258 Operationally, in a dictionary-passing implementation, the
1259 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1260 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1261 extract it on pattern matching.
1265 Notice the way that the syntax fits smoothly with that used for
1266 universal quantification earlier.
1272 <title>Record Constructors</title>
1275 GHC allows existentials to be used with records syntax as well. For example:
1278 data Counter a = forall self. NewCounter
1280 , _inc :: self -> self
1281 , _display :: self -> IO ()
1285 Here <literal>tag</literal> is a public field, with a well-typed selector
1286 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1287 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1288 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1289 compile-time error. In other words, <emphasis>GHC defines a record selector function
1290 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1291 (This example used an underscore in the fields for which record selectors
1292 will not be defined, but that is only programming style; GHC ignores them.)
1296 To make use of these hidden fields, we need to create some helper functions:
1299 inc :: Counter a -> Counter a
1300 inc (NewCounter x i d t) = NewCounter
1301 { _this = i x, _inc = i, _display = d, tag = t }
1303 display :: Counter a -> IO ()
1304 display NewCounter{ _this = x, _display = d } = d x
1307 Now we can define counters with different underlying implementations:
1310 counterA :: Counter String
1311 counterA = NewCounter
1312 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1314 counterB :: Counter String
1315 counterB = NewCounter
1316 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1319 display (inc counterA) -- prints "1"
1320 display (inc (inc counterB)) -- prints "##"
1323 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1324 <literal>forall</literal> may be omitted. For example, we can express
1325 the same <literal>Counter a</literal> using GADT:
1328 data Counter a where
1329 NewCounter { _this :: self
1330 , _inc :: self -> self
1331 , _display :: self -> IO ()
1337 At the moment, record update syntax is only supported for Haskell 98 data types,
1338 so the following function does <emphasis>not</emphasis> work:
1341 -- This is invalid; use explicit NewCounter instead for now
1342 setTag :: Counter a -> a -> Counter a
1343 setTag obj t = obj{ tag = t }
1352 <title>Restrictions</title>
1355 There are several restrictions on the ways in which existentially-quantified
1356 constructors can be use.
1365 When pattern matching, each pattern match introduces a new,
1366 distinct, type for each existential type variable. These types cannot
1367 be unified with any other type, nor can they escape from the scope of
1368 the pattern match. For example, these fragments are incorrect:
1376 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1377 is the result of <function>f1</function>. One way to see why this is wrong is to
1378 ask what type <function>f1</function> has:
1382 f1 :: Foo -> a -- Weird!
1386 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1391 f1 :: forall a. Foo -> a -- Wrong!
1395 The original program is just plain wrong. Here's another sort of error
1399 f2 (Baz1 a b) (Baz1 p q) = a==q
1403 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1404 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1405 from the two <function>Baz1</function> constructors.
1413 You can't pattern-match on an existentially quantified
1414 constructor in a <literal>let</literal> or <literal>where</literal> group of
1415 bindings. So this is illegal:
1419 f3 x = a==b where { Baz1 a b = x }
1422 Instead, use a <literal>case</literal> expression:
1425 f3 x = case x of Baz1 a b -> a==b
1428 In general, you can only pattern-match
1429 on an existentially-quantified constructor in a <literal>case</literal> expression or
1430 in the patterns of a function definition.
1432 The reason for this restriction is really an implementation one.
1433 Type-checking binding groups is already a nightmare without
1434 existentials complicating the picture. Also an existential pattern
1435 binding at the top level of a module doesn't make sense, because it's
1436 not clear how to prevent the existentially-quantified type "escaping".
1437 So for now, there's a simple-to-state restriction. We'll see how
1445 You can't use existential quantification for <literal>newtype</literal>
1446 declarations. So this is illegal:
1450 newtype T = forall a. Ord a => MkT a
1454 Reason: a value of type <literal>T</literal> must be represented as a
1455 pair of a dictionary for <literal>Ord t</literal> and a value of type
1456 <literal>t</literal>. That contradicts the idea that
1457 <literal>newtype</literal> should have no concrete representation.
1458 You can get just the same efficiency and effect by using
1459 <literal>data</literal> instead of <literal>newtype</literal>. If
1460 there is no overloading involved, then there is more of a case for
1461 allowing an existentially-quantified <literal>newtype</literal>,
1462 because the <literal>data</literal> version does carry an
1463 implementation cost, but single-field existentially quantified
1464 constructors aren't much use. So the simple restriction (no
1465 existential stuff on <literal>newtype</literal>) stands, unless there
1466 are convincing reasons to change it.
1474 You can't use <literal>deriving</literal> to define instances of a
1475 data type with existentially quantified data constructors.
1477 Reason: in most cases it would not make sense. For example:#
1480 data T = forall a. MkT [a] deriving( Eq )
1483 To derive <literal>Eq</literal> in the standard way we would need to have equality
1484 between the single component of two <function>MkT</function> constructors:
1488 (MkT a) == (MkT b) = ???
1491 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1492 It's just about possible to imagine examples in which the derived instance
1493 would make sense, but it seems altogether simpler simply to prohibit such
1494 declarations. Define your own instances!
1509 <sect2 id="multi-param-type-classes">
1510 <title>Class declarations</title>
1513 This section, and the next one, documents GHC's type-class extensions.
1514 There's lots of background in the paper <ulink
1515 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1516 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1517 Jones, Erik Meijer).
1520 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1524 <title>Multi-parameter type classes</title>
1526 Multi-parameter type classes are permitted. For example:
1530 class Collection c a where
1531 union :: c a -> c a -> c a
1539 <title>The superclasses of a class declaration</title>
1542 There are no restrictions on the context in a class declaration
1543 (which introduces superclasses), except that the class hierarchy must
1544 be acyclic. So these class declarations are OK:
1548 class Functor (m k) => FiniteMap m k where
1551 class (Monad m, Monad (t m)) => Transform t m where
1552 lift :: m a -> (t m) a
1558 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1559 of "acyclic" involves only the superclass relationships. For example,
1565 op :: D b => a -> b -> b
1568 class C a => D a where { ... }
1572 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1573 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1574 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1581 <sect3 id="class-method-types">
1582 <title>Class method types</title>
1585 Haskell 98 prohibits class method types to mention constraints on the
1586 class type variable, thus:
1589 fromList :: [a] -> s a
1590 elem :: Eq a => a -> s a -> Bool
1592 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1593 contains the constraint <literal>Eq a</literal>, constrains only the
1594 class type variable (in this case <literal>a</literal>).
1595 GHC lifts this restriction.
1602 <sect2 id="functional-dependencies">
1603 <title>Functional dependencies
1606 <para> Functional dependencies are implemented as described by Mark Jones
1607 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1608 In Proceedings of the 9th European Symposium on Programming,
1609 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1613 Functional dependencies are introduced by a vertical bar in the syntax of a
1614 class declaration; e.g.
1616 class (Monad m) => MonadState s m | m -> s where ...
1618 class Foo a b c | a b -> c where ...
1620 There should be more documentation, but there isn't (yet). Yell if you need it.
1623 <sect3><title>Rules for functional dependencies </title>
1625 In a class declaration, all of the class type variables must be reachable (in the sense
1626 mentioned in <xref linkend="type-restrictions"/>)
1627 from the free variables of each method type.
1631 class Coll s a where
1633 insert :: s -> a -> s
1636 is not OK, because the type of <literal>empty</literal> doesn't mention
1637 <literal>a</literal>. Functional dependencies can make the type variable
1640 class Coll s a | s -> a where
1642 insert :: s -> a -> s
1645 Alternatively <literal>Coll</literal> might be rewritten
1648 class Coll s a where
1650 insert :: s a -> a -> s a
1654 which makes the connection between the type of a collection of
1655 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1656 Occasionally this really doesn't work, in which case you can split the
1664 class CollE s => Coll s a where
1665 insert :: s -> a -> s
1672 <title>Background on functional dependencies</title>
1674 <para>The following description of the motivation and use of functional dependencies is taken
1675 from the Hugs user manual, reproduced here (with minor changes) by kind
1676 permission of Mark Jones.
1679 Consider the following class, intended as part of a
1680 library for collection types:
1682 class Collects e ce where
1684 insert :: e -> ce -> ce
1685 member :: e -> ce -> Bool
1687 The type variable e used here represents the element type, while ce is the type
1688 of the container itself. Within this framework, we might want to define
1689 instances of this class for lists or characteristic functions (both of which
1690 can be used to represent collections of any equality type), bit sets (which can
1691 be used to represent collections of characters), or hash tables (which can be
1692 used to represent any collection whose elements have a hash function). Omitting
1693 standard implementation details, this would lead to the following declarations:
1695 instance Eq e => Collects e [e] where ...
1696 instance Eq e => Collects e (e -> Bool) where ...
1697 instance Collects Char BitSet where ...
1698 instance (Hashable e, Collects a ce)
1699 => Collects e (Array Int ce) where ...
1701 All this looks quite promising; we have a class and a range of interesting
1702 implementations. Unfortunately, there are some serious problems with the class
1703 declaration. First, the empty function has an ambiguous type:
1705 empty :: Collects e ce => ce
1707 By "ambiguous" we mean that there is a type variable e that appears on the left
1708 of the <literal>=></literal> symbol, but not on the right. The problem with
1709 this is that, according to the theoretical foundations of Haskell overloading,
1710 we cannot guarantee a well-defined semantics for any term with an ambiguous
1714 We can sidestep this specific problem by removing the empty member from the
1715 class declaration. However, although the remaining members, insert and member,
1716 do not have ambiguous types, we still run into problems when we try to use
1717 them. For example, consider the following two functions:
1719 f x y = insert x . insert y
1722 for which GHC infers the following types:
1724 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1725 g :: (Collects Bool c, Collects Char c) => c -> c
1727 Notice that the type for f allows the two parameters x and y to be assigned
1728 different types, even though it attempts to insert each of the two values, one
1729 after the other, into the same collection. If we're trying to model collections
1730 that contain only one type of value, then this is clearly an inaccurate
1731 type. Worse still, the definition for g is accepted, without causing a type
1732 error. As a result, the error in this code will not be flagged at the point
1733 where it appears. Instead, it will show up only when we try to use g, which
1734 might even be in a different module.
1737 <sect4><title>An attempt to use constructor classes</title>
1740 Faced with the problems described above, some Haskell programmers might be
1741 tempted to use something like the following version of the class declaration:
1743 class Collects e c where
1745 insert :: e -> c e -> c e
1746 member :: e -> c e -> Bool
1748 The key difference here is that we abstract over the type constructor c that is
1749 used to form the collection type c e, and not over that collection type itself,
1750 represented by ce in the original class declaration. This avoids the immediate
1751 problems that we mentioned above: empty has type <literal>Collects e c => c
1752 e</literal>, which is not ambiguous.
1755 The function f from the previous section has a more accurate type:
1757 f :: (Collects e c) => e -> e -> c e -> c e
1759 The function g from the previous section is now rejected with a type error as
1760 we would hope because the type of f does not allow the two arguments to have
1762 This, then, is an example of a multiple parameter class that does actually work
1763 quite well in practice, without ambiguity problems.
1764 There is, however, a catch. This version of the Collects class is nowhere near
1765 as general as the original class seemed to be: only one of the four instances
1766 for <literal>Collects</literal>
1767 given above can be used with this version of Collects because only one of
1768 them---the instance for lists---has a collection type that can be written in
1769 the form c e, for some type constructor c, and element type e.
1773 <sect4><title>Adding functional dependencies</title>
1776 To get a more useful version of the Collects class, Hugs provides a mechanism
1777 that allows programmers to specify dependencies between the parameters of a
1778 multiple parameter class (For readers with an interest in theoretical
1779 foundations and previous work: The use of dependency information can be seen
1780 both as a generalization of the proposal for `parametric type classes' that was
1781 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1782 later framework for "improvement" of qualified types. The
1783 underlying ideas are also discussed in a more theoretical and abstract setting
1784 in a manuscript [implparam], where they are identified as one point in a
1785 general design space for systems of implicit parameterization.).
1787 To start with an abstract example, consider a declaration such as:
1789 class C a b where ...
1791 which tells us simply that C can be thought of as a binary relation on types
1792 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1793 included in the definition of classes to add information about dependencies
1794 between parameters, as in the following examples:
1796 class D a b | a -> b where ...
1797 class E a b | a -> b, b -> a where ...
1799 The notation <literal>a -> b</literal> used here between the | and where
1800 symbols --- not to be
1801 confused with a function type --- indicates that the a parameter uniquely
1802 determines the b parameter, and might be read as "a determines b." Thus D is
1803 not just a relation, but actually a (partial) function. Similarly, from the two
1804 dependencies that are included in the definition of E, we can see that E
1805 represents a (partial) one-one mapping between types.
1808 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
1809 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
1810 m>=0, meaning that the y parameters are uniquely determined by the x
1811 parameters. Spaces can be used as separators if more than one variable appears
1812 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
1813 annotated with multiple dependencies using commas as separators, as in the
1814 definition of E above. Some dependencies that we can write in this notation are
1815 redundant, and will be rejected because they don't serve any useful
1816 purpose, and may instead indicate an error in the program. Examples of
1817 dependencies like this include <literal>a -> a </literal>,
1818 <literal>a -> a a </literal>,
1819 <literal>a -> </literal>, etc. There can also be
1820 some redundancy if multiple dependencies are given, as in
1821 <literal>a->b</literal>,
1822 <literal>b->c </literal>, <literal>a->c </literal>, and
1823 in which some subset implies the remaining dependencies. Examples like this are
1824 not treated as errors. Note that dependencies appear only in class
1825 declarations, and not in any other part of the language. In particular, the
1826 syntax for instance declarations, class constraints, and types is completely
1830 By including dependencies in a class declaration, we provide a mechanism for
1831 the programmer to specify each multiple parameter class more precisely. The
1832 compiler, on the other hand, is responsible for ensuring that the set of
1833 instances that are in scope at any given point in the program is consistent
1834 with any declared dependencies. For example, the following pair of instance
1835 declarations cannot appear together in the same scope because they violate the
1836 dependency for D, even though either one on its own would be acceptable:
1838 instance D Bool Int where ...
1839 instance D Bool Char where ...
1841 Note also that the following declaration is not allowed, even by itself:
1843 instance D [a] b where ...
1845 The problem here is that this instance would allow one particular choice of [a]
1846 to be associated with more than one choice for b, which contradicts the
1847 dependency specified in the definition of D. More generally, this means that,
1848 in any instance of the form:
1850 instance D t s where ...
1852 for some particular types t and s, the only variables that can appear in s are
1853 the ones that appear in t, and hence, if the type t is known, then s will be
1854 uniquely determined.
1857 The benefit of including dependency information is that it allows us to define
1858 more general multiple parameter classes, without ambiguity problems, and with
1859 the benefit of more accurate types. To illustrate this, we return to the
1860 collection class example, and annotate the original definition of <literal>Collects</literal>
1861 with a simple dependency:
1863 class Collects e ce | ce -> e where
1865 insert :: e -> ce -> ce
1866 member :: e -> ce -> Bool
1868 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
1869 determined by the type of the collection ce. Note that both parameters of
1870 Collects are of kind *; there are no constructor classes here. Note too that
1871 all of the instances of Collects that we gave earlier can be used
1872 together with this new definition.
1875 What about the ambiguity problems that we encountered with the original
1876 definition? The empty function still has type Collects e ce => ce, but it is no
1877 longer necessary to regard that as an ambiguous type: Although the variable e
1878 does not appear on the right of the => symbol, the dependency for class
1879 Collects tells us that it is uniquely determined by ce, which does appear on
1880 the right of the => symbol. Hence the context in which empty is used can still
1881 give enough information to determine types for both ce and e, without
1882 ambiguity. More generally, we need only regard a type as ambiguous if it
1883 contains a variable on the left of the => that is not uniquely determined
1884 (either directly or indirectly) by the variables on the right.
1887 Dependencies also help to produce more accurate types for user defined
1888 functions, and hence to provide earlier detection of errors, and less cluttered
1889 types for programmers to work with. Recall the previous definition for a
1892 f x y = insert x y = insert x . insert y
1894 for which we originally obtained a type:
1896 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1898 Given the dependency information that we have for Collects, however, we can
1899 deduce that a and b must be equal because they both appear as the second
1900 parameter in a Collects constraint with the same first parameter c. Hence we
1901 can infer a shorter and more accurate type for f:
1903 f :: (Collects a c) => a -> a -> c -> c
1905 In a similar way, the earlier definition of g will now be flagged as a type error.
1908 Although we have given only a few examples here, it should be clear that the
1909 addition of dependency information can help to make multiple parameter classes
1910 more useful in practice, avoiding ambiguity problems, and allowing more general
1911 sets of instance declarations.
1917 <sect2 id="instance-decls">
1918 <title>Instance declarations</title>
1920 <sect3 id="instance-rules">
1921 <title>Relaxed rules for instance declarations</title>
1923 <para>An instance declaration has the form
1925 instance ( <replaceable>assertion</replaceable><subscript>1</subscript>, ..., <replaceable>assertion</replaceable><subscript>n</subscript>) => <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
1927 The part before the "<literal>=></literal>" is the
1928 <emphasis>context</emphasis>, while the part after the
1929 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
1933 In Haskell 98 the head of an instance declaration
1934 must be of the form <literal>C (T a1 ... an)</literal>, where
1935 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1936 and the <literal>a1 ... an</literal> are distinct type variables.
1937 Furthermore, the assertions in the context of the instance declaration
1938 must be of the form <literal>C a</literal> where <literal>a</literal>
1939 is a type variable that occurs in the head.
1942 The <option>-fglasgow-exts</option> flag loosens these restrictions
1943 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1944 the context and head of the instance declaration can each consist of arbitrary
1945 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1949 For each assertion in the context:
1951 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1952 <listitem><para>The assertion has fewer constructors and variables (taken together
1953 and counting repetitions) than the head</para></listitem>
1957 <listitem><para>The coverage condition. For each functional dependency,
1958 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
1959 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
1960 every type variable in
1961 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
1962 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
1963 substitution mapping each type variable in the class declaration to the
1964 corresponding type in the instance declaration.
1967 These restrictions ensure that context reduction terminates: each reduction
1968 step makes the problem smaller by at least one
1969 constructor. For example, the following would make the type checker
1970 loop if it wasn't excluded:
1972 instance C a => C a where ...
1974 For example, these are OK:
1976 instance C Int [a] -- Multiple parameters
1977 instance Eq (S [a]) -- Structured type in head
1979 -- Repeated type variable in head
1980 instance C4 a a => C4 [a] [a]
1981 instance Stateful (ST s) (MutVar s)
1983 -- Head can consist of type variables only
1985 instance (Eq a, Show b) => C2 a b
1987 -- Non-type variables in context
1988 instance Show (s a) => Show (Sized s a)
1989 instance C2 Int a => C3 Bool [a]
1990 instance C2 Int a => C3 [a] b
1994 -- Context assertion no smaller than head
1995 instance C a => C a where ...
1996 -- (C b b) has more more occurrences of b than the head
1997 instance C b b => Foo [b] where ...
2002 The same restrictions apply to instances generated by
2003 <literal>deriving</literal> clauses. Thus the following is accepted:
2005 data MinHeap h a = H a (h a)
2008 because the derived instance
2010 instance (Show a, Show (h a)) => Show (MinHeap h a)
2012 conforms to the above rules.
2016 A useful idiom permitted by the above rules is as follows.
2017 If one allows overlapping instance declarations then it's quite
2018 convenient to have a "default instance" declaration that applies if
2019 something more specific does not:
2027 <sect3 id="undecidable-instances">
2028 <title>Undecidable instances</title>
2031 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2032 For example, sometimes you might want to use the following to get the
2033 effect of a "class synonym":
2035 class (C1 a, C2 a, C3 a) => C a where { }
2037 instance (C1 a, C2 a, C3 a) => C a where { }
2039 This allows you to write shorter signatures:
2045 f :: (C1 a, C2 a, C3 a) => ...
2047 The restrictions on functional dependencies (<xref
2048 linkend="functional-dependencies"/>) are particularly troublesome.
2049 It is tempting to introduce type variables in the context that do not appear in
2050 the head, something that is excluded by the normal rules. For example:
2052 class HasConverter a b | a -> b where
2055 data Foo a = MkFoo a
2057 instance (HasConverter a b,Show b) => Show (Foo a) where
2058 show (MkFoo value) = show (convert value)
2060 This is dangerous territory, however. Here, for example, is a program that would make the
2065 instance F [a] [[a]]
2066 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2068 Similarly, it can be tempting to lift the coverage condition:
2070 class Mul a b c | a b -> c where
2071 (.*.) :: a -> b -> c
2073 instance Mul Int Int Int where (.*.) = (*)
2074 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2075 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2077 The third instance declaration does not obey the coverage condition;
2078 and indeed the (somewhat strange) definition:
2080 f = \ b x y -> if b then x .*. [y] else y
2082 makes instance inference go into a loop, because it requires the constraint
2083 <literal>(Mul a [b] b)</literal>.
2086 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2087 the experimental flag <option>-fallow-undecidable-instances</option>
2088 <indexterm><primary>-fallow-undecidable-instances
2089 option</primary></indexterm>, you can use arbitrary
2090 types in both an instance context and instance head. Termination is ensured by having a
2091 fixed-depth recursion stack. If you exceed the stack depth you get a
2092 sort of backtrace, and the opportunity to increase the stack depth
2093 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2099 <sect3 id="instance-overlap">
2100 <title>Overlapping instances</title>
2102 In general, <emphasis>GHC requires that that it be unambiguous which instance
2104 should be used to resolve a type-class constraint</emphasis>. This behaviour
2105 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2106 <indexterm><primary>-fallow-overlapping-instances
2107 </primary></indexterm>
2108 and <option>-fallow-incoherent-instances</option>
2109 <indexterm><primary>-fallow-incoherent-instances
2110 </primary></indexterm>, as this section discusses. Both these
2111 flags are dynamic flags, and can be set on a per-module basis, using
2112 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2114 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2115 it tries to match every instance declaration against the
2117 by instantiating the head of the instance declaration. For example, consider
2120 instance context1 => C Int a where ... -- (A)
2121 instance context2 => C a Bool where ... -- (B)
2122 instance context3 => C Int [a] where ... -- (C)
2123 instance context4 => C Int [Int] where ... -- (D)
2125 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2126 but (C) and (D) do not. When matching, GHC takes
2127 no account of the context of the instance declaration
2128 (<literal>context1</literal> etc).
2129 GHC's default behaviour is that <emphasis>exactly one instance must match the
2130 constraint it is trying to resolve</emphasis>.
2131 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2132 including both declarations (A) and (B), say); an error is only reported if a
2133 particular constraint matches more than one.
2137 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2138 more than one instance to match, provided there is a most specific one. For
2139 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2140 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2141 most-specific match, the program is rejected.
2144 However, GHC is conservative about committing to an overlapping instance. For example:
2149 Suppose that from the RHS of <literal>f</literal> we get the constraint
2150 <literal>C Int [b]</literal>. But
2151 GHC does not commit to instance (C), because in a particular
2152 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2153 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2154 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2155 GHC will instead pick (C), without complaining about
2156 the problem of subsequent instantiations.
2159 The willingness to be overlapped or incoherent is a property of
2160 the <emphasis>instance declaration</emphasis> itself, controlled by the
2161 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2162 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2163 being defined. Neither flag is required in a module that imports and uses the
2164 instance declaration. Specifically, during the lookup process:
2167 An instance declaration is ignored during the lookup process if (a) a more specific
2168 match is found, and (b) the instance declaration was compiled with
2169 <option>-fallow-overlapping-instances</option>. The flag setting for the
2170 more-specific instance does not matter.
2173 Suppose an instance declaration does not matche the constraint being looked up, but
2174 does unify with it, so that it might match when the constraint is further
2175 instantiated. Usually GHC will regard this as a reason for not committing to
2176 some other constraint. But if the instance declaration was compiled with
2177 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2178 check for that declaration.
2181 All this makes it possible for a library author to design a library that relies on
2182 overlapping instances without the library client having to know.
2184 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2185 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2190 <title>Type synonyms in the instance head</title>
2193 <emphasis>Unlike Haskell 98, instance heads may use type
2194 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2195 As always, using a type synonym is just shorthand for
2196 writing the RHS of the type synonym definition. For example:
2200 type Point = (Int,Int)
2201 instance C Point where ...
2202 instance C [Point] where ...
2206 is legal. However, if you added
2210 instance C (Int,Int) where ...
2214 as well, then the compiler will complain about the overlapping
2215 (actually, identical) instance declarations. As always, type synonyms
2216 must be fully applied. You cannot, for example, write:
2221 instance Monad P where ...
2225 This design decision is independent of all the others, and easily
2226 reversed, but it makes sense to me.
2234 <sect2 id="type-restrictions">
2235 <title>Type signatures</title>
2237 <sect3><title>The context of a type signature</title>
2239 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2240 the form <emphasis>(class type-variable)</emphasis> or
2241 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2242 these type signatures are perfectly OK
2245 g :: Ord (T a ()) => ...
2249 GHC imposes the following restrictions on the constraints in a type signature.
2253 forall tv1..tvn (c1, ...,cn) => type
2256 (Here, we write the "foralls" explicitly, although the Haskell source
2257 language omits them; in Haskell 98, all the free type variables of an
2258 explicit source-language type signature are universally quantified,
2259 except for the class type variables in a class declaration. However,
2260 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2269 <emphasis>Each universally quantified type variable
2270 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2272 A type variable <literal>a</literal> is "reachable" if it it appears
2273 in the same constraint as either a type variable free in in
2274 <literal>type</literal>, or another reachable type variable.
2275 A value with a type that does not obey
2276 this reachability restriction cannot be used without introducing
2277 ambiguity; that is why the type is rejected.
2278 Here, for example, is an illegal type:
2282 forall a. Eq a => Int
2286 When a value with this type was used, the constraint <literal>Eq tv</literal>
2287 would be introduced where <literal>tv</literal> is a fresh type variable, and
2288 (in the dictionary-translation implementation) the value would be
2289 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2290 can never know which instance of <literal>Eq</literal> to use because we never
2291 get any more information about <literal>tv</literal>.
2295 that the reachability condition is weaker than saying that <literal>a</literal> is
2296 functionally dependent on a type variable free in
2297 <literal>type</literal> (see <xref
2298 linkend="functional-dependencies"/>). The reason for this is there
2299 might be a "hidden" dependency, in a superclass perhaps. So
2300 "reachable" is a conservative approximation to "functionally dependent".
2301 For example, consider:
2303 class C a b | a -> b where ...
2304 class C a b => D a b where ...
2305 f :: forall a b. D a b => a -> a
2307 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2308 but that is not immediately apparent from <literal>f</literal>'s type.
2314 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2315 universally quantified type variables <literal>tvi</literal></emphasis>.
2317 For example, this type is OK because <literal>C a b</literal> mentions the
2318 universally quantified type variable <literal>b</literal>:
2322 forall a. C a b => burble
2326 The next type is illegal because the constraint <literal>Eq b</literal> does not
2327 mention <literal>a</literal>:
2331 forall a. Eq b => burble
2335 The reason for this restriction is milder than the other one. The
2336 excluded types are never useful or necessary (because the offending
2337 context doesn't need to be witnessed at this point; it can be floated
2338 out). Furthermore, floating them out increases sharing. Lastly,
2339 excluding them is a conservative choice; it leaves a patch of
2340 territory free in case we need it later.
2351 <title>For-all hoisting</title>
2353 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2354 end of an arrow, thus:
2356 type Discard a = forall b. a -> b -> a
2358 g :: Int -> Discard Int
2361 Simply expanding the type synonym would give
2363 g :: Int -> (forall b. Int -> b -> Int)
2365 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2367 g :: forall b. Int -> Int -> b -> Int
2369 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2370 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2371 performs the transformation:</emphasis>
2373 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2375 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2377 (In fact, GHC tries to retain as much synonym information as possible for use in
2378 error messages, but that is a usability issue.) This rule applies, of course, whether
2379 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2380 valid way to write <literal>g</literal>'s type signature:
2382 g :: Int -> Int -> forall b. b -> Int
2386 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2389 type Foo a = (?x::Int) => Bool -> a
2394 g :: (?x::Int) => Bool -> Bool -> Int
2402 <sect2 id="implicit-parameters">
2403 <title>Implicit parameters</title>
2405 <para> Implicit parameters are implemented as described in
2406 "Implicit parameters: dynamic scoping with static types",
2407 J Lewis, MB Shields, E Meijer, J Launchbury,
2408 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2412 <para>(Most of the following, stil rather incomplete, documentation is
2413 due to Jeff Lewis.)</para>
2415 <para>Implicit parameter support is enabled with the option
2416 <option>-fimplicit-params</option>.</para>
2419 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2420 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2421 context. In Haskell, all variables are statically bound. Dynamic
2422 binding of variables is a notion that goes back to Lisp, but was later
2423 discarded in more modern incarnations, such as Scheme. Dynamic binding
2424 can be very confusing in an untyped language, and unfortunately, typed
2425 languages, in particular Hindley-Milner typed languages like Haskell,
2426 only support static scoping of variables.
2429 However, by a simple extension to the type class system of Haskell, we
2430 can support dynamic binding. Basically, we express the use of a
2431 dynamically bound variable as a constraint on the type. These
2432 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2433 function uses a dynamically-bound variable <literal>?x</literal>
2434 of type <literal>t'</literal>". For
2435 example, the following expresses the type of a sort function,
2436 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2438 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2440 The dynamic binding constraints are just a new form of predicate in the type class system.
2443 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2444 where <literal>x</literal> is
2445 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2446 Use of this construct also introduces a new
2447 dynamic-binding constraint in the type of the expression.
2448 For example, the following definition
2449 shows how we can define an implicitly parameterized sort function in
2450 terms of an explicitly parameterized <literal>sortBy</literal> function:
2452 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2454 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2460 <title>Implicit-parameter type constraints</title>
2462 Dynamic binding constraints behave just like other type class
2463 constraints in that they are automatically propagated. Thus, when a
2464 function is used, its implicit parameters are inherited by the
2465 function that called it. For example, our <literal>sort</literal> function might be used
2466 to pick out the least value in a list:
2468 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2469 least xs = fst (sort xs)
2471 Without lifting a finger, the <literal>?cmp</literal> parameter is
2472 propagated to become a parameter of <literal>least</literal> as well. With explicit
2473 parameters, the default is that parameters must always be explicit
2474 propagated. With implicit parameters, the default is to always
2478 An implicit-parameter type constraint differs from other type class constraints in the
2479 following way: All uses of a particular implicit parameter must have
2480 the same type. This means that the type of <literal>(?x, ?x)</literal>
2481 is <literal>(?x::a) => (a,a)</literal>, and not
2482 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2486 <para> You can't have an implicit parameter in the context of a class or instance
2487 declaration. For example, both these declarations are illegal:
2489 class (?x::Int) => C a where ...
2490 instance (?x::a) => Foo [a] where ...
2492 Reason: exactly which implicit parameter you pick up depends on exactly where
2493 you invoke a function. But the ``invocation'' of instance declarations is done
2494 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2495 Easiest thing is to outlaw the offending types.</para>
2497 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2499 f :: (?x :: [a]) => Int -> Int
2502 g :: (Read a, Show a) => String -> String
2505 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2506 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2507 quite unambiguous, and fixes the type <literal>a</literal>.
2512 <title>Implicit-parameter bindings</title>
2515 An implicit parameter is <emphasis>bound</emphasis> using the standard
2516 <literal>let</literal> or <literal>where</literal> binding forms.
2517 For example, we define the <literal>min</literal> function by binding
2518 <literal>cmp</literal>.
2521 min = let ?cmp = (<=) in least
2525 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2526 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2527 (including in a list comprehension, or do-notation, or pattern guards),
2528 or a <literal>where</literal> clause.
2529 Note the following points:
2532 An implicit-parameter binding group must be a
2533 collection of simple bindings to implicit-style variables (no
2534 function-style bindings, and no type signatures); these bindings are
2535 neither polymorphic or recursive.
2538 You may not mix implicit-parameter bindings with ordinary bindings in a
2539 single <literal>let</literal>
2540 expression; use two nested <literal>let</literal>s instead.
2541 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2545 You may put multiple implicit-parameter bindings in a
2546 single binding group; but they are <emphasis>not</emphasis> treated
2547 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2548 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2549 parameter. The bindings are not nested, and may be re-ordered without changing
2550 the meaning of the program.
2551 For example, consider:
2553 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2555 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2556 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2558 f :: (?x::Int) => Int -> Int
2566 <sect3><title>Implicit parameters and polymorphic recursion</title>
2569 Consider these two definitions:
2572 len1 xs = let ?acc = 0 in len_acc1 xs
2575 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2580 len2 xs = let ?acc = 0 in len_acc2 xs
2582 len_acc2 :: (?acc :: Int) => [a] -> Int
2584 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2586 The only difference between the two groups is that in the second group
2587 <literal>len_acc</literal> is given a type signature.
2588 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2589 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2590 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2591 has a type signature, the recursive call is made to the
2592 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2593 as an implicit parameter. So we get the following results in GHCi:
2600 Adding a type signature dramatically changes the result! This is a rather
2601 counter-intuitive phenomenon, worth watching out for.
2605 <sect3><title>Implicit parameters and monomorphism</title>
2607 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2608 Haskell Report) to implicit parameters. For example, consider:
2616 Since the binding for <literal>y</literal> falls under the Monomorphism
2617 Restriction it is not generalised, so the type of <literal>y</literal> is
2618 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2619 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2620 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2621 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2622 <literal>y</literal> in the body of the <literal>let</literal> will see the
2623 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2624 <literal>14</literal>.
2629 <sect2 id="linear-implicit-parameters">
2630 <title>Linear implicit parameters</title>
2632 Linear implicit parameters are an idea developed by Koen Claessen,
2633 Mark Shields, and Simon PJ. They address the long-standing
2634 problem that monads seem over-kill for certain sorts of problem, notably:
2637 <listitem> <para> distributing a supply of unique names </para> </listitem>
2638 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2639 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2643 Linear implicit parameters are just like ordinary implicit parameters,
2644 except that they are "linear" -- that is, they cannot be copied, and
2645 must be explicitly "split" instead. Linear implicit parameters are
2646 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2647 (The '/' in the '%' suggests the split!)
2652 import GHC.Exts( Splittable )
2654 data NameSupply = ...
2656 splitNS :: NameSupply -> (NameSupply, NameSupply)
2657 newName :: NameSupply -> Name
2659 instance Splittable NameSupply where
2663 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2664 f env (Lam x e) = Lam x' (f env e)
2667 env' = extend env x x'
2668 ...more equations for f...
2670 Notice that the implicit parameter %ns is consumed
2672 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2673 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2677 So the translation done by the type checker makes
2678 the parameter explicit:
2680 f :: NameSupply -> Env -> Expr -> Expr
2681 f ns env (Lam x e) = Lam x' (f ns1 env e)
2683 (ns1,ns2) = splitNS ns
2685 env = extend env x x'
2687 Notice the call to 'split' introduced by the type checker.
2688 How did it know to use 'splitNS'? Because what it really did
2689 was to introduce a call to the overloaded function 'split',
2690 defined by the class <literal>Splittable</literal>:
2692 class Splittable a where
2695 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2696 split for name supplies. But we can simply write
2702 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2704 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2705 <literal>GHC.Exts</literal>.
2710 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2711 are entirely distinct implicit parameters: you
2712 can use them together and they won't intefere with each other. </para>
2715 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2717 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2718 in the context of a class or instance declaration. </para></listitem>
2722 <sect3><title>Warnings</title>
2725 The monomorphism restriction is even more important than usual.
2726 Consider the example above:
2728 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2729 f env (Lam x e) = Lam x' (f env e)
2732 env' = extend env x x'
2734 If we replaced the two occurrences of x' by (newName %ns), which is
2735 usually a harmless thing to do, we get:
2737 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2738 f env (Lam x e) = Lam (newName %ns) (f env e)
2740 env' = extend env x (newName %ns)
2742 But now the name supply is consumed in <emphasis>three</emphasis> places
2743 (the two calls to newName,and the recursive call to f), so
2744 the result is utterly different. Urk! We don't even have
2748 Well, this is an experimental change. With implicit
2749 parameters we have already lost beta reduction anyway, and
2750 (as John Launchbury puts it) we can't sensibly reason about
2751 Haskell programs without knowing their typing.
2756 <sect3><title>Recursive functions</title>
2757 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2760 foo :: %x::T => Int -> [Int]
2762 foo n = %x : foo (n-1)
2764 where T is some type in class Splittable.</para>
2766 Do you get a list of all the same T's or all different T's
2767 (assuming that split gives two distinct T's back)?
2769 If you supply the type signature, taking advantage of polymorphic
2770 recursion, you get what you'd probably expect. Here's the
2771 translated term, where the implicit param is made explicit:
2774 foo x n = let (x1,x2) = split x
2775 in x1 : foo x2 (n-1)
2777 But if you don't supply a type signature, GHC uses the Hindley
2778 Milner trick of using a single monomorphic instance of the function
2779 for the recursive calls. That is what makes Hindley Milner type inference
2780 work. So the translation becomes
2784 foom n = x : foom (n-1)
2788 Result: 'x' is not split, and you get a list of identical T's. So the
2789 semantics of the program depends on whether or not foo has a type signature.
2792 You may say that this is a good reason to dislike linear implicit parameters
2793 and you'd be right. That is why they are an experimental feature.
2799 <sect2 id="sec-kinding">
2800 <title>Explicitly-kinded quantification</title>
2803 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2804 to give the kind explicitly as (machine-checked) documentation,
2805 just as it is nice to give a type signature for a function. On some occasions,
2806 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2807 John Hughes had to define the data type:
2809 data Set cxt a = Set [a]
2810 | Unused (cxt a -> ())
2812 The only use for the <literal>Unused</literal> constructor was to force the correct
2813 kind for the type variable <literal>cxt</literal>.
2816 GHC now instead allows you to specify the kind of a type variable directly, wherever
2817 a type variable is explicitly bound. Namely:
2819 <listitem><para><literal>data</literal> declarations:
2821 data Set (cxt :: * -> *) a = Set [a]
2822 </screen></para></listitem>
2823 <listitem><para><literal>type</literal> declarations:
2825 type T (f :: * -> *) = f Int
2826 </screen></para></listitem>
2827 <listitem><para><literal>class</literal> declarations:
2829 class (Eq a) => C (f :: * -> *) a where ...
2830 </screen></para></listitem>
2831 <listitem><para><literal>forall</literal>'s in type signatures:
2833 f :: forall (cxt :: * -> *). Set cxt Int
2834 </screen></para></listitem>
2839 The parentheses are required. Some of the spaces are required too, to
2840 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2841 will get a parse error, because "<literal>::*->*</literal>" is a
2842 single lexeme in Haskell.
2846 As part of the same extension, you can put kind annotations in types
2849 f :: (Int :: *) -> Int
2850 g :: forall a. a -> (a :: *)
2854 atype ::= '(' ctype '::' kind ')
2856 The parentheses are required.
2861 <sect2 id="universal-quantification">
2862 <title>Arbitrary-rank polymorphism
2866 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2867 allows us to say exactly what this means. For example:
2875 g :: forall b. (b -> b)
2877 The two are treated identically.
2881 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2882 explicit universal quantification in
2884 For example, all the following types are legal:
2886 f1 :: forall a b. a -> b -> a
2887 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2889 f2 :: (forall a. a->a) -> Int -> Int
2890 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2892 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2894 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2895 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2896 The <literal>forall</literal> makes explicit the universal quantification that
2897 is implicitly added by Haskell.
2900 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2901 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2902 shows, the polymorphic type on the left of the function arrow can be overloaded.
2905 The function <literal>f3</literal> has a rank-3 type;
2906 it has rank-2 types on the left of a function arrow.
2909 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2910 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2911 that restriction has now been lifted.)
2912 In particular, a forall-type (also called a "type scheme"),
2913 including an operational type class context, is legal:
2915 <listitem> <para> On the left of a function arrow </para> </listitem>
2916 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2917 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2918 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2919 field type signatures.</para> </listitem>
2920 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2921 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2923 There is one place you cannot put a <literal>forall</literal>:
2924 you cannot instantiate a type variable with a forall-type. So you cannot
2925 make a forall-type the argument of a type constructor. So these types are illegal:
2927 x1 :: [forall a. a->a]
2928 x2 :: (forall a. a->a, Int)
2929 x3 :: Maybe (forall a. a->a)
2931 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2932 a type variable any more!
2941 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2942 the types of the constructor arguments. Here are several examples:
2948 data T a = T1 (forall b. b -> b -> b) a
2950 data MonadT m = MkMonad { return :: forall a. a -> m a,
2951 bind :: forall a b. m a -> (a -> m b) -> m b
2954 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2960 The constructors have rank-2 types:
2966 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2967 MkMonad :: forall m. (forall a. a -> m a)
2968 -> (forall a b. m a -> (a -> m b) -> m b)
2970 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2976 Notice that you don't need to use a <literal>forall</literal> if there's an
2977 explicit context. For example in the first argument of the
2978 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2979 prefixed to the argument type. The implicit <literal>forall</literal>
2980 quantifies all type variables that are not already in scope, and are
2981 mentioned in the type quantified over.
2985 As for type signatures, implicit quantification happens for non-overloaded
2986 types too. So if you write this:
2989 data T a = MkT (Either a b) (b -> b)
2992 it's just as if you had written this:
2995 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2998 That is, since the type variable <literal>b</literal> isn't in scope, it's
2999 implicitly universally quantified. (Arguably, it would be better
3000 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3001 where that is what is wanted. Feedback welcomed.)
3005 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3006 the constructor to suitable values, just as usual. For example,
3017 a3 = MkSwizzle reverse
3020 a4 = let r x = Just x
3027 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3028 mkTs f x y = [T1 f x, T1 f y]
3034 The type of the argument can, as usual, be more general than the type
3035 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3036 does not need the <literal>Ord</literal> constraint.)
3040 When you use pattern matching, the bound variables may now have
3041 polymorphic types. For example:
3047 f :: T a -> a -> (a, Char)
3048 f (T1 w k) x = (w k x, w 'c' 'd')
3050 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3051 g (MkSwizzle s) xs f = s (map f (s xs))
3053 h :: MonadT m -> [m a] -> m [a]
3054 h m [] = return m []
3055 h m (x:xs) = bind m x $ \y ->
3056 bind m (h m xs) $ \ys ->
3063 In the function <function>h</function> we use the record selectors <literal>return</literal>
3064 and <literal>bind</literal> to extract the polymorphic bind and return functions
3065 from the <literal>MonadT</literal> data structure, rather than using pattern
3071 <title>Type inference</title>
3074 In general, type inference for arbitrary-rank types is undecidable.
3075 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3076 to get a decidable algorithm by requiring some help from the programmer.
3077 We do not yet have a formal specification of "some help" but the rule is this:
3080 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3081 provides an explicit polymorphic type for x, or GHC's type inference will assume
3082 that x's type has no foralls in it</emphasis>.
3085 What does it mean to "provide" an explicit type for x? You can do that by
3086 giving a type signature for x directly, using a pattern type signature
3087 (<xref linkend="scoped-type-variables"/>), thus:
3089 \ f :: (forall a. a->a) -> (f True, f 'c')
3091 Alternatively, you can give a type signature to the enclosing
3092 context, which GHC can "push down" to find the type for the variable:
3094 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3096 Here the type signature on the expression can be pushed inwards
3097 to give a type signature for f. Similarly, and more commonly,
3098 one can give a type signature for the function itself:
3100 h :: (forall a. a->a) -> (Bool,Char)
3101 h f = (f True, f 'c')
3103 You don't need to give a type signature if the lambda bound variable
3104 is a constructor argument. Here is an example we saw earlier:
3106 f :: T a -> a -> (a, Char)
3107 f (T1 w k) x = (w k x, w 'c' 'd')
3109 Here we do not need to give a type signature to <literal>w</literal>, because
3110 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3117 <sect3 id="implicit-quant">
3118 <title>Implicit quantification</title>
3121 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3122 user-written types, if and only if there is no explicit <literal>forall</literal>,
3123 GHC finds all the type variables mentioned in the type that are not already
3124 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3128 f :: forall a. a -> a
3135 h :: forall b. a -> b -> b
3141 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3144 f :: (a -> a) -> Int
3146 f :: forall a. (a -> a) -> Int
3148 f :: (forall a. a -> a) -> Int
3151 g :: (Ord a => a -> a) -> Int
3152 -- MEANS the illegal type
3153 g :: forall a. (Ord a => a -> a) -> Int
3155 g :: (forall a. Ord a => a -> a) -> Int
3157 The latter produces an illegal type, which you might think is silly,
3158 but at least the rule is simple. If you want the latter type, you
3159 can write your for-alls explicitly. Indeed, doing so is strongly advised
3168 <sect2 id="scoped-type-variables">
3169 <title>Scoped type variables
3173 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3175 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3176 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3177 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
3181 f (xs::[a]) = ys ++ ys
3186 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
3187 This brings the type variable <literal>a</literal> into scope; it scopes over
3188 all the patterns and right hand sides for this equation for <function>f</function>.
3189 In particular, it is in scope at the type signature for <varname>y</varname>.
3193 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
3194 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
3195 implicitly universally quantified. (If there are no type variables in
3196 scope, all type variables mentioned in the signature are universally
3197 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
3198 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
3199 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
3200 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3201 it becomes possible to do so.
3205 Scoped type variables are implemented in both GHC and Hugs. Where the
3206 implementations differ from the specification below, those differences
3211 So much for the basic idea. Here are the details.
3215 <title>What a scoped type variable means</title>
3217 A lexically-scoped type variable is simply
3218 the name for a type. The restriction it expresses is that all occurrences
3219 of the same name mean the same type. For example:
3221 f :: [Int] -> Int -> Int
3222 f (xs::[a]) (y::a) = (head xs + y) :: a
3224 The pattern type signatures on the left hand side of
3225 <literal>f</literal> express the fact that <literal>xs</literal>
3226 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
3227 must have this same type. The type signature on the expression <literal>(head xs)</literal>
3228 specifies that this expression must have the same type <literal>a</literal>.
3229 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
3230 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
3231 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
3232 rules, which specified that a pattern-bound type variable should be universally quantified.)
3233 For example, all of these are legal:</para>
3236 t (x::a) (y::a) = x+y*2
3238 f (x::a) (y::b) = [x,y] -- a unifies with b
3240 g (x::a) = x + 1::Int -- a unifies with Int
3242 h x = let k (y::a) = [x,y] -- a is free in the
3243 in k x -- environment
3245 k (x::a) True = ... -- a unifies with Int
3246 k (x::Int) False = ...
3249 w (x::a) = x -- a unifies with [b]
3255 <title>Scope and implicit quantification</title>
3263 All the type variables mentioned in a pattern,
3264 that are not already in scope,
3265 are brought into scope by the pattern. We describe this set as
3266 the <emphasis>type variables bound by the pattern</emphasis>.
3269 f (x::a) = let g (y::(a,b)) = fst y
3273 The pattern <literal>(x::a)</literal> brings the type variable
3274 <literal>a</literal> into scope, as well as the term
3275 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
3276 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
3277 and brings into scope the type variable <literal>b</literal>.
3283 The type variable(s) bound by the pattern have the same scope
3284 as the term variable(s) bound by the pattern. For example:
3287 f (x::a) = <...rhs of f...>
3288 (p::b, q::b) = (1,2)
3289 in <...body of let...>
3291 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
3292 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
3293 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
3294 just like <literal>p</literal> and <literal>q</literal> do.
3295 Indeed, the newly bound type variables also scope over any ordinary, separate
3296 type signatures in the <literal>let</literal> group.
3303 The type variables bound by the pattern may be
3304 mentioned in ordinary type signatures or pattern
3305 type signatures anywhere within their scope.
3312 In ordinary type signatures, any type variable mentioned in the
3313 signature that is in scope is <emphasis>not</emphasis> universally quantified.
3321 Ordinary type signatures do not bring any new type variables
3322 into scope (except in the type signature itself!). So this is illegal:
3329 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
3330 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
3331 and that is an incorrect typing.
3338 The pattern type signature is a monotype:
3343 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
3347 The type variables bound by a pattern type signature can only be instantiated to monotypes,
3348 not to type schemes.
3352 There is no implicit universal quantification on pattern type signatures (in contrast to
3353 ordinary type signatures).
3363 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3364 scope over the methods defined in the <literal>where</literal> part. For example:
3378 (Not implemented in Hugs yet, Dec 98).
3388 <sect3 id="decl-type-sigs">
3389 <title>Declaration type signatures</title>
3390 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3391 quantification (using <literal>forall</literal>) brings into scope the
3392 explicitly-quantified
3393 type variables, in the definition of the named function(s). For example:
3395 f :: forall a. [a] -> [a]
3396 f (x:xs) = xs ++ [ x :: a ]
3398 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3399 the definition of "<literal>f</literal>".
3401 <para>This only happens if the quantification in <literal>f</literal>'s type
3402 signature is explicit. For example:
3405 g (x:xs) = xs ++ [ x :: a ]
3407 This program will be rejected, because "<literal>a</literal>" does not scope
3408 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3409 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3410 quantification rules.
3414 <sect3 id="pattern-type-sigs">
3415 <title>Where a pattern type signature can occur</title>
3418 A pattern type signature can occur in any pattern. For example:
3423 A pattern type signature can be on an arbitrary sub-pattern, not
3428 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3437 Pattern type signatures, including the result part, can be used
3438 in lambda abstractions:
3441 (\ (x::a, y) :: a -> x)
3448 Pattern type signatures, including the result part, can be used
3449 in <literal>case</literal> expressions:
3452 case e of { ((x::a, y) :: (a,b)) -> x }
3455 Note that the <literal>-></literal> symbol in a case alternative
3456 leads to difficulties when parsing a type signature in the pattern: in
3457 the absence of the extra parentheses in the example above, the parser
3458 would try to interpret the <literal>-></literal> as a function
3459 arrow and give a parse error later.
3467 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3468 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3469 token or a parenthesised type of some sort). To see why,
3470 consider how one would parse this:
3484 Pattern type signatures can bind existential type variables.
3489 data T = forall a. MkT [a]
3492 f (MkT [t::a]) = MkT t3
3505 Pattern type signatures
3506 can be used in pattern bindings:
3509 f x = let (y, z::a) = x in ...
3510 f1 x = let (y, z::Int) = x in ...
3511 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3512 f3 :: (b->b) = \x -> x
3515 In all such cases, the binding is not generalised over the pattern-bound
3516 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3517 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3518 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3519 In contrast, the binding
3524 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3525 in <literal>f4</literal>'s scope.
3531 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3532 type signatures. The two can be used independently or together.</para>
3536 <sect3 id="result-type-sigs">
3537 <title>Result type signatures</title>
3540 The result type of a function can be given a signature, thus:
3544 f (x::a) :: [a] = [x,x,x]
3548 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3549 result type. Sometimes this is the only way of naming the type variable
3554 f :: Int -> [a] -> [a]
3555 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3556 in \xs -> map g (reverse xs `zip` xs)
3561 The type variables bound in a result type signature scope over the right hand side
3562 of the definition. However, consider this corner-case:
3564 rev1 :: [a] -> [a] = \xs -> reverse xs
3566 foo ys = rev (ys::[a])
3568 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3569 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3570 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3571 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3572 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3575 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3576 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3580 rev1 :: [a] -> [a] = \xs -> reverse xs
3585 Result type signatures are not yet implemented in Hugs.
3592 <sect2 id="deriving-typeable">
3593 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3596 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3597 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3598 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3599 classes <literal>Eq</literal>, <literal>Ord</literal>,
3600 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3603 GHC extends this list with two more classes that may be automatically derived
3604 (provided the <option>-fglasgow-exts</option> flag is specified):
3605 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3606 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3607 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3609 <para>An instance of <literal>Typeable</literal> can only be derived if the
3610 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3611 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3613 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3614 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3616 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3617 are used, and only <literal>Typeable1</literal> up to
3618 <literal>Typeable7</literal> are provided in the library.)
3619 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3620 class, whose kind suits that of the data type constructor, and
3621 then writing the data type instance by hand.
3625 <sect2 id="newtype-deriving">
3626 <title>Generalised derived instances for newtypes</title>
3629 When you define an abstract type using <literal>newtype</literal>, you may want
3630 the new type to inherit some instances from its representation. In
3631 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3632 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3633 other classes you have to write an explicit instance declaration. For
3634 example, if you define
3637 newtype Dollars = Dollars Int
3640 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3641 explicitly define an instance of <literal>Num</literal>:
3644 instance Num Dollars where
3645 Dollars a + Dollars b = Dollars (a+b)
3648 All the instance does is apply and remove the <literal>newtype</literal>
3649 constructor. It is particularly galling that, since the constructor
3650 doesn't appear at run-time, this instance declaration defines a
3651 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3652 dictionary, only slower!
3656 <sect3> <title> Generalising the deriving clause </title>
3658 GHC now permits such instances to be derived instead, so one can write
3660 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3663 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3664 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3665 derives an instance declaration of the form
3668 instance Num Int => Num Dollars
3671 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3675 We can also derive instances of constructor classes in a similar
3676 way. For example, suppose we have implemented state and failure monad
3677 transformers, such that
3680 instance Monad m => Monad (State s m)
3681 instance Monad m => Monad (Failure m)
3683 In Haskell 98, we can define a parsing monad by
3685 type Parser tok m a = State [tok] (Failure m) a
3688 which is automatically a monad thanks to the instance declarations
3689 above. With the extension, we can make the parser type abstract,
3690 without needing to write an instance of class <literal>Monad</literal>, via
3693 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3696 In this case the derived instance declaration is of the form
3698 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3701 Notice that, since <literal>Monad</literal> is a constructor class, the
3702 instance is a <emphasis>partial application</emphasis> of the new type, not the
3703 entire left hand side. We can imagine that the type declaration is
3704 ``eta-converted'' to generate the context of the instance
3709 We can even derive instances of multi-parameter classes, provided the
3710 newtype is the last class parameter. In this case, a ``partial
3711 application'' of the class appears in the <literal>deriving</literal>
3712 clause. For example, given the class
3715 class StateMonad s m | m -> s where ...
3716 instance Monad m => StateMonad s (State s m) where ...
3718 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3720 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3721 deriving (Monad, StateMonad [tok])
3724 The derived instance is obtained by completing the application of the
3725 class to the new type:
3728 instance StateMonad [tok] (State [tok] (Failure m)) =>
3729 StateMonad [tok] (Parser tok m)
3734 As a result of this extension, all derived instances in newtype
3735 declarations are treated uniformly (and implemented just by reusing
3736 the dictionary for the representation type), <emphasis>except</emphasis>
3737 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3738 the newtype and its representation.
3742 <sect3> <title> A more precise specification </title>
3744 Derived instance declarations are constructed as follows. Consider the
3745 declaration (after expansion of any type synonyms)
3748 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3754 The type <literal>t</literal> is an arbitrary type
3757 The <literal>vk+1...vn</literal> are type variables which do not occur in
3758 <literal>t</literal>, and
3761 The <literal>ci</literal> are partial applications of
3762 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3763 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3766 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3767 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3768 should not "look through" the type or its constructor. You can still
3769 derive these classes for a newtype, but it happens in the usual way, not
3770 via this new mechanism.
3773 Then, for each <literal>ci</literal>, the derived instance
3776 instance ci (t vk+1...v) => ci (T v1...vp)
3778 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3779 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3783 As an example which does <emphasis>not</emphasis> work, consider
3785 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3787 Here we cannot derive the instance
3789 instance Monad (State s m) => Monad (NonMonad m)
3792 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3793 and so cannot be "eta-converted" away. It is a good thing that this
3794 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3795 not, in fact, a monad --- for the same reason. Try defining
3796 <literal>>>=</literal> with the correct type: you won't be able to.
3800 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3801 important, since we can only derive instances for the last one. If the
3802 <literal>StateMonad</literal> class above were instead defined as
3805 class StateMonad m s | m -> s where ...
3808 then we would not have been able to derive an instance for the
3809 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3810 classes usually have one "main" parameter for which deriving new
3811 instances is most interesting.
3813 <para>Lastly, all of this applies only for classes other than
3814 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3815 and <literal>Data</literal>, for which the built-in derivation applies (section
3816 4.3.3. of the Haskell Report).
3817 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3818 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3819 the standard method is used or the one described here.)
3825 <sect2 id="typing-binds">
3826 <title>Generalised typing of mutually recursive bindings</title>
3829 The Haskell Report specifies that a group of bindings (at top level, or in a
3830 <literal>let</literal> or <literal>where</literal>) should be sorted into
3831 strongly-connected components, and then type-checked in dependency order
3832 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3833 Report, Section 4.5.1</ulink>).
3834 As each group is type-checked, any binders of the group that
3836 an explicit type signature are put in the type environment with the specified
3838 and all others are monomorphic until the group is generalised
3839 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3842 <para>Following a suggestion of Mark Jones, in his paper
3843 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3845 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3847 <emphasis>the dependency analysis ignores references to variables that have an explicit
3848 type signature</emphasis>.
3849 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3850 typecheck. For example, consider:
3852 f :: Eq a => a -> Bool
3853 f x = (x == x) || g True || g "Yes"
3855 g y = (y <= y) || f True
3857 This is rejected by Haskell 98, but under Jones's scheme the definition for
3858 <literal>g</literal> is typechecked first, separately from that for
3859 <literal>f</literal>,
3860 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3861 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3862 type is generalised, to get
3864 g :: Ord a => a -> Bool
3866 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3867 <literal>g</literal> in the type environment.
3871 The same refined dependency analysis also allows the type signatures of
3872 mutually-recursive functions to have different contexts, something that is illegal in
3873 Haskell 98 (Section 4.5.2, last sentence). With
3874 <option>-fglasgow-exts</option>
3875 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3876 type signatures; in practice this means that only variables bound by the same
3877 pattern binding must have the same context. For example, this is fine:
3879 f :: Eq a => a -> Bool
3880 f x = (x == x) || g True
3882 g :: Ord a => a -> Bool
3883 g y = (y <= y) || f True
3889 <!-- ==================== End of type system extensions ================= -->
3891 <!-- ====================== Generalised algebraic data types ======================= -->
3894 <title>Generalised Algebraic Data Types</title>
3896 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3897 to give the type signatures of constructors explicitly. For example:
3900 Lit :: Int -> Term Int
3901 Succ :: Term Int -> Term Int
3902 IsZero :: Term Int -> Term Bool
3903 If :: Term Bool -> Term a -> Term a -> Term a
3904 Pair :: Term a -> Term b -> Term (a,b)
3906 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3907 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3908 for these <literal>Terms</literal>:
3912 eval (Succ t) = 1 + eval t
3913 eval (IsZero t) = eval t == 0
3914 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3915 eval (Pair e1 e2) = (eval e1, eval e2)
3917 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3919 <para> The extensions to GHC are these:
3922 Data type declarations have a 'where' form, as exemplified above. The type signature of
3923 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3924 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3925 have no scope. Indeed, one can write a kind signature instead:
3927 data Term :: * -> * where ...
3929 or even a mixture of the two:
3931 data Foo a :: (* -> *) -> * where ...
3933 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3936 data Foo a (b :: * -> *) where ...
3941 There are no restrictions on the type of the data constructor, except that the result
3942 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3943 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3947 You can use record syntax on a GADT-style data type declaration:
3951 Lit { val :: Int } :: Term Int
3952 Succ { num :: Term Int } :: Term Int
3953 Pred { num :: Term Int } :: Term Int
3954 IsZero { arg :: Term Int } :: Term Bool
3955 Pair { arg1 :: Term a
3958 If { cnd :: Term Bool
3963 For every constructor that has a field <literal>f</literal>, (a) the type of
3964 field <literal>f</literal> must be the same; and (b) the
3965 result type of the constructor must be the same; both modulo alpha conversion.
3966 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
3968 single name. Although their field types are both <literal>Term Int</literal>,
3969 their selector functions actually have different types:
3972 num :: Term Int -> Term Int
3973 arg :: Term Bool -> Term Int
3976 At the moment, record updates are not yet possible with GADT, so support is
3977 limited to record construction, selection and pattern matching:
3980 someTerm :: Term Bool
3981 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
3984 eval Lit { val = i } = i
3985 eval Succ { num = t } = eval t + 1
3986 eval Pred { num = t } = eval t - 1
3987 eval IsZero { arg = t } = eval t == 0
3988 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
3989 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
3995 You can use strictness annotations, in the obvious places
3996 in the constructor type:
3999 Lit :: !Int -> Term Int
4000 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
4001 Pair :: Term a -> Term b -> Term (a,b)
4006 You can use a <literal>deriving</literal> clause on a GADT-style data type
4007 declaration, but only if the data type could also have been declared in
4008 Haskell-98 syntax. For example, these two declarations are equivalent
4010 data Maybe1 a where {
4011 Nothing1 :: Maybe a ;
4012 Just1 :: a -> Maybe a
4013 } deriving( Eq, Ord )
4015 data Maybe2 a = Nothing2 | Just2 a
4018 This simply allows you to declare a vanilla Haskell-98 data type using the
4019 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
4023 Pattern matching causes type refinement. For example, in the right hand side of the equation
4028 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
4029 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
4030 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
4032 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
4033 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
4034 occur. However, the refinement is quite general. For example, if we had:
4036 eval :: Term a -> a -> a
4037 eval (Lit i) j = i+j
4039 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
4040 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
4041 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
4047 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
4049 data T a = forall b. MkT b (b->a)
4050 data T' a where { MKT :: b -> (b->a) -> T' a }
4055 <!-- ====================== End of Generalised algebraic data types ======================= -->
4057 <!-- ====================== TEMPLATE HASKELL ======================= -->
4059 <sect1 id="template-haskell">
4060 <title>Template Haskell</title>
4062 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
4063 Template Haskell at <ulink url="http://www.haskell.org/th/">
4064 http://www.haskell.org/th/</ulink>, while
4066 the main technical innovations is discussed in "<ulink
4067 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4068 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4069 The details of the Template Haskell design are still in flux. Make sure you
4070 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
4071 (search for the type ExpQ).
4072 [Temporary: many changes to the original design are described in
4073 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4074 Not all of these changes are in GHC 6.2.]
4077 <para> The first example from that paper is set out below as a worked example to help get you started.
4081 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4082 Tim Sheard is going to expand it.)
4086 <title>Syntax</title>
4088 <para> Template Haskell has the following new syntactic
4089 constructions. You need to use the flag
4090 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4091 </indexterm>to switch these syntactic extensions on
4092 (<option>-fth</option> is no longer implied by
4093 <option>-fglasgow-exts</option>).</para>
4097 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4098 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4099 There must be no space between the "$" and the identifier or parenthesis. This use
4100 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4101 of "." as an infix operator. If you want the infix operator, put spaces around it.
4103 <para> A splice can occur in place of
4105 <listitem><para> an expression; the spliced expression must
4106 have type <literal>Q Exp</literal></para></listitem>
4107 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4108 <listitem><para> [Planned, but not implemented yet.] a
4109 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4111 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4112 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4118 A expression quotation is written in Oxford brackets, thus:
4120 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4121 the quotation has type <literal>Expr</literal>.</para></listitem>
4122 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4123 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4124 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4125 the quotation has type <literal>Type</literal>.</para></listitem>
4126 </itemizedlist></para></listitem>
4129 Reification is written thus:
4131 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4132 has type <literal>Dec</literal>. </para></listitem>
4133 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4134 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4135 <listitem><para> Still to come: fixities </para></listitem>
4137 </itemizedlist></para>
4144 <sect2> <title> Using Template Haskell </title>
4148 The data types and monadic constructor functions for Template Haskell are in the library
4149 <literal>Language.Haskell.THSyntax</literal>.
4153 You can only run a function at compile time if it is imported from another module. That is,
4154 you can't define a function in a module, and call it from within a splice in the same module.
4155 (It would make sense to do so, but it's hard to implement.)
4159 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4162 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4163 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4164 compiles and runs a program, and then looks at the result. So it's important that
4165 the program it compiles produces results whose representations are identical to
4166 those of the compiler itself.
4170 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4171 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4176 <sect2> <title> A Template Haskell Worked Example </title>
4177 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4178 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4185 -- Import our template "pr"
4186 import Printf ( pr )
4188 -- The splice operator $ takes the Haskell source code
4189 -- generated at compile time by "pr" and splices it into
4190 -- the argument of "putStrLn".
4191 main = putStrLn ( $(pr "Hello") )
4197 -- Skeletal printf from the paper.
4198 -- It needs to be in a separate module to the one where
4199 -- you intend to use it.
4201 -- Import some Template Haskell syntax
4202 import Language.Haskell.TH
4204 -- Describe a format string
4205 data Format = D | S | L String
4207 -- Parse a format string. This is left largely to you
4208 -- as we are here interested in building our first ever
4209 -- Template Haskell program and not in building printf.
4210 parse :: String -> [Format]
4213 -- Generate Haskell source code from a parsed representation
4214 -- of the format string. This code will be spliced into
4215 -- the module which calls "pr", at compile time.
4216 gen :: [Format] -> ExpQ
4217 gen [D] = [| \n -> show n |]
4218 gen [S] = [| \s -> s |]
4219 gen [L s] = stringE s
4221 -- Here we generate the Haskell code for the splice
4222 -- from an input format string.
4223 pr :: String -> ExpQ
4224 pr s = gen (parse s)
4227 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4230 $ ghc --make -fth main.hs -o main.exe
4233 <para>Run "main.exe" and here is your output:</para>
4243 <title>Using Template Haskell with Profiling</title>
4244 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4246 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4247 interpreter to run the splice expressions. The bytecode interpreter
4248 runs the compiled expression on top of the same runtime on which GHC
4249 itself is running; this means that the compiled code referred to by
4250 the interpreted expression must be compatible with this runtime, and
4251 in particular this means that object code that is compiled for
4252 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4253 expression, because profiled object code is only compatible with the
4254 profiling version of the runtime.</para>
4256 <para>This causes difficulties if you have a multi-module program
4257 containing Template Haskell code and you need to compile it for
4258 profiling, because GHC cannot load the profiled object code and use it
4259 when executing the splices. Fortunately GHC provides a workaround.
4260 The basic idea is to compile the program twice:</para>
4264 <para>Compile the program or library first the normal way, without
4265 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4268 <para>Then compile it again with <option>-prof</option>, and
4269 additionally use <option>-osuf
4270 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4271 to name the object files differentliy (you can choose any suffix
4272 that isn't the normal object suffix here). GHC will automatically
4273 load the object files built in the first step when executing splice
4274 expressions. If you omit the <option>-osuf</option> flag when
4275 building with <option>-prof</option> and Template Haskell is used,
4276 GHC will emit an error message. </para>
4283 <!-- ===================== Arrow notation =================== -->
4285 <sect1 id="arrow-notation">
4286 <title>Arrow notation
4289 <para>Arrows are a generalization of monads introduced by John Hughes.
4290 For more details, see
4295 “Generalising Monads to Arrows”,
4296 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4297 pp67–111, May 2000.
4303 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4304 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4310 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4311 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4317 and the arrows web page at
4318 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4319 With the <option>-farrows</option> flag, GHC supports the arrow
4320 notation described in the second of these papers.
4321 What follows is a brief introduction to the notation;
4322 it won't make much sense unless you've read Hughes's paper.
4323 This notation is translated to ordinary Haskell,
4324 using combinators from the
4325 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4329 <para>The extension adds a new kind of expression for defining arrows:
4331 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4332 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4334 where <literal>proc</literal> is a new keyword.
4335 The variables of the pattern are bound in the body of the
4336 <literal>proc</literal>-expression,
4337 which is a new sort of thing called a <firstterm>command</firstterm>.
4338 The syntax of commands is as follows:
4340 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4341 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4342 | <replaceable>cmd</replaceable><superscript>0</superscript>
4344 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4345 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4346 infix operators as for expressions, and
4348 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4349 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4350 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4351 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4352 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4353 | <replaceable>fcmd</replaceable>
4355 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4356 | ( <replaceable>cmd</replaceable> )
4357 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4359 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4360 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4361 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4362 | <replaceable>cmd</replaceable>
4364 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4365 except that the bodies are commands instead of expressions.
4369 Commands produce values, but (like monadic computations)
4370 may yield more than one value,
4371 or none, and may do other things as well.
4372 For the most part, familiarity with monadic notation is a good guide to
4374 However the values of expressions, even monadic ones,
4375 are determined by the values of the variables they contain;
4376 this is not necessarily the case for commands.
4380 A simple example of the new notation is the expression
4382 proc x -> f -< x+1
4384 We call this a <firstterm>procedure</firstterm> or
4385 <firstterm>arrow abstraction</firstterm>.
4386 As with a lambda expression, the variable <literal>x</literal>
4387 is a new variable bound within the <literal>proc</literal>-expression.
4388 It refers to the input to the arrow.
4389 In the above example, <literal>-<</literal> is not an identifier but an
4390 new reserved symbol used for building commands from an expression of arrow
4391 type and an expression to be fed as input to that arrow.
4392 (The weird look will make more sense later.)
4393 It may be read as analogue of application for arrows.
4394 The above example is equivalent to the Haskell expression
4396 arr (\ x -> x+1) >>> f
4398 That would make no sense if the expression to the left of
4399 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4400 More generally, the expression to the left of <literal>-<</literal>
4401 may not involve any <firstterm>local variable</firstterm>,
4402 i.e. a variable bound in the current arrow abstraction.
4403 For such a situation there is a variant <literal>-<<</literal>, as in
4405 proc x -> f x -<< x+1
4407 which is equivalent to
4409 arr (\ x -> (f x, x+1)) >>> app
4411 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4413 Such an arrow is equivalent to a monad, so if you're using this form
4414 you may find a monadic formulation more convenient.
4418 <title>do-notation for commands</title>
4421 Another form of command is a form of <literal>do</literal>-notation.
4422 For example, you can write
4431 You can read this much like ordinary <literal>do</literal>-notation,
4432 but with commands in place of monadic expressions.
4433 The first line sends the value of <literal>x+1</literal> as an input to
4434 the arrow <literal>f</literal>, and matches its output against
4435 <literal>y</literal>.
4436 In the next line, the output is discarded.
4437 The arrow <function>returnA</function> is defined in the
4438 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4439 module as <literal>arr id</literal>.
4440 The above example is treated as an abbreviation for
4442 arr (\ x -> (x, x)) >>>
4443 first (arr (\ x -> x+1) >>> f) >>>
4444 arr (\ (y, x) -> (y, (x, y))) >>>
4445 first (arr (\ y -> 2*y) >>> g) >>>
4447 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4448 first (arr (\ (x, z) -> x*z) >>> h) >>>
4449 arr (\ (t, z) -> t+z) >>>
4452 Note that variables not used later in the composition are projected out.
4453 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4455 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4456 module, this reduces to
4458 arr (\ x -> (x+1, x)) >>>
4460 arr (\ (y, x) -> (2*y, (x, y))) >>>
4462 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4464 arr (\ (t, z) -> t+z)
4466 which is what you might have written by hand.
4467 With arrow notation, GHC keeps track of all those tuples of variables for you.
4471 Note that although the above translation suggests that
4472 <literal>let</literal>-bound variables like <literal>z</literal> must be
4473 monomorphic, the actual translation produces Core,
4474 so polymorphic variables are allowed.
4478 It's also possible to have mutually recursive bindings,
4479 using the new <literal>rec</literal> keyword, as in the following example:
4481 counter :: ArrowCircuit a => a Bool Int
4482 counter = proc reset -> do
4483 rec output <- returnA -< if reset then 0 else next
4484 next <- delay 0 -< output+1
4485 returnA -< output
4487 The translation of such forms uses the <function>loop</function> combinator,
4488 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4494 <title>Conditional commands</title>
4497 In the previous example, we used a conditional expression to construct the
4499 Sometimes we want to conditionally execute different commands, as in
4506 which is translated to
4508 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4509 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4511 Since the translation uses <function>|||</function>,
4512 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4516 There are also <literal>case</literal> commands, like
4522 y <- h -< (x1, x2)
4526 The syntax is the same as for <literal>case</literal> expressions,
4527 except that the bodies of the alternatives are commands rather than expressions.
4528 The translation is similar to that of <literal>if</literal> commands.
4534 <title>Defining your own control structures</title>
4537 As we're seen, arrow notation provides constructs,
4538 modelled on those for expressions,
4539 for sequencing, value recursion and conditionals.
4540 But suitable combinators,
4541 which you can define in ordinary Haskell,
4542 may also be used to build new commands out of existing ones.
4543 The basic idea is that a command defines an arrow from environments to values.
4544 These environments assign values to the free local variables of the command.
4545 Thus combinators that produce arrows from arrows
4546 may also be used to build commands from commands.
4547 For example, the <literal>ArrowChoice</literal> class includes a combinator
4549 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4551 so we can use it to build commands:
4553 expr' = proc x -> do
4556 symbol Plus -< ()
4557 y <- term -< ()
4560 symbol Minus -< ()
4561 y <- term -< ()
4564 (The <literal>do</literal> on the first line is needed to prevent the first
4565 <literal><+> ...</literal> from being interpreted as part of the
4566 expression on the previous line.)
4567 This is equivalent to
4569 expr' = (proc x -> returnA -< x)
4570 <+> (proc x -> do
4571 symbol Plus -< ()
4572 y <- term -< ()
4574 <+> (proc x -> do
4575 symbol Minus -< ()
4576 y <- term -< ()
4579 It is essential that this operator be polymorphic in <literal>e</literal>
4580 (representing the environment input to the command
4581 and thence to its subcommands)
4582 and satisfy the corresponding naturality property
4584 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4586 at least for strict <literal>k</literal>.
4587 (This should be automatic if you're not using <function>seq</function>.)
4588 This ensures that environments seen by the subcommands are environments
4589 of the whole command,
4590 and also allows the translation to safely trim these environments.
4591 The operator must also not use any variable defined within the current
4596 We could define our own operator
4598 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4599 untilA body cond = proc x ->
4600 if cond x then returnA -< ()
4603 untilA body cond -< x
4605 and use it in the same way.
4606 Of course this infix syntax only makes sense for binary operators;
4607 there is also a more general syntax involving special brackets:
4611 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4618 <title>Primitive constructs</title>
4621 Some operators will need to pass additional inputs to their subcommands.
4622 For example, in an arrow type supporting exceptions,
4623 the operator that attaches an exception handler will wish to pass the
4624 exception that occurred to the handler.
4625 Such an operator might have a type
4627 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4629 where <literal>Ex</literal> is the type of exceptions handled.
4630 You could then use this with arrow notation by writing a command
4632 body `handleA` \ ex -> handler
4634 so that if an exception is raised in the command <literal>body</literal>,
4635 the variable <literal>ex</literal> is bound to the value of the exception
4636 and the command <literal>handler</literal>,
4637 which typically refers to <literal>ex</literal>, is entered.
4638 Though the syntax here looks like a functional lambda,
4639 we are talking about commands, and something different is going on.
4640 The input to the arrow represented by a command consists of values for
4641 the free local variables in the command, plus a stack of anonymous values.
4642 In all the prior examples, this stack was empty.
4643 In the second argument to <function>handleA</function>,
4644 this stack consists of one value, the value of the exception.
4645 The command form of lambda merely gives this value a name.
4650 the values on the stack are paired to the right of the environment.
4651 So operators like <function>handleA</function> that pass
4652 extra inputs to their subcommands can be designed for use with the notation
4653 by pairing the values with the environment in this way.
4654 More precisely, the type of each argument of the operator (and its result)
4655 should have the form
4657 a (...(e,t1), ... tn) t
4659 where <replaceable>e</replaceable> is a polymorphic variable
4660 (representing the environment)
4661 and <replaceable>ti</replaceable> are the types of the values on the stack,
4662 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4663 The polymorphic variable <replaceable>e</replaceable> must not occur in
4664 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4665 <replaceable>t</replaceable>.
4666 However the arrows involved need not be the same.
4667 Here are some more examples of suitable operators:
4669 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4670 runReader :: ... => a e c -> a' (e,State) c
4671 runState :: ... => a e c -> a' (e,State) (c,State)
4673 We can supply the extra input required by commands built with the last two
4674 by applying them to ordinary expressions, as in
4678 (|runReader (do { ... })|) s
4680 which adds <literal>s</literal> to the stack of inputs to the command
4681 built using <function>runReader</function>.
4685 The command versions of lambda abstraction and application are analogous to
4686 the expression versions.
4687 In particular, the beta and eta rules describe equivalences of commands.
4688 These three features (operators, lambda abstraction and application)
4689 are the core of the notation; everything else can be built using them,
4690 though the results would be somewhat clumsy.
4691 For example, we could simulate <literal>do</literal>-notation by defining
4693 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4694 u `bind` f = returnA &&& u >>> f
4696 bind_ :: Arrow a => a e b -> a e c -> a e c
4697 u `bind_` f = u `bind` (arr fst >>> f)
4699 We could simulate <literal>if</literal> by defining
4701 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4702 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4709 <title>Differences with the paper</title>
4714 <para>Instead of a single form of arrow application (arrow tail) with two
4715 translations, the implementation provides two forms
4716 <quote><literal>-<</literal></quote> (first-order)
4717 and <quote><literal>-<<</literal></quote> (higher-order).
4722 <para>User-defined operators are flagged with banana brackets instead of
4723 a new <literal>form</literal> keyword.
4732 <title>Portability</title>
4735 Although only GHC implements arrow notation directly,
4736 there is also a preprocessor
4738 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4739 that translates arrow notation into Haskell 98
4740 for use with other Haskell systems.
4741 You would still want to check arrow programs with GHC;
4742 tracing type errors in the preprocessor output is not easy.
4743 Modules intended for both GHC and the preprocessor must observe some
4744 additional restrictions:
4749 The module must import
4750 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4756 The preprocessor cannot cope with other Haskell extensions.
4757 These would have to go in separate modules.
4763 Because the preprocessor targets Haskell (rather than Core),
4764 <literal>let</literal>-bound variables are monomorphic.
4775 <!-- ==================== ASSERTIONS ================= -->
4777 <sect1 id="sec-assertions">
4779 <indexterm><primary>Assertions</primary></indexterm>
4783 If you want to make use of assertions in your standard Haskell code, you
4784 could define a function like the following:
4790 assert :: Bool -> a -> a
4791 assert False x = error "assertion failed!"
4798 which works, but gives you back a less than useful error message --
4799 an assertion failed, but which and where?
4803 One way out is to define an extended <function>assert</function> function which also
4804 takes a descriptive string to include in the error message and
4805 perhaps combine this with the use of a pre-processor which inserts
4806 the source location where <function>assert</function> was used.
4810 Ghc offers a helping hand here, doing all of this for you. For every
4811 use of <function>assert</function> in the user's source:
4817 kelvinToC :: Double -> Double
4818 kelvinToC k = assert (k >= 0.0) (k+273.15)
4824 Ghc will rewrite this to also include the source location where the
4831 assert pred val ==> assertError "Main.hs|15" pred val
4837 The rewrite is only performed by the compiler when it spots
4838 applications of <function>Control.Exception.assert</function>, so you
4839 can still define and use your own versions of
4840 <function>assert</function>, should you so wish. If not, import
4841 <literal>Control.Exception</literal> to make use
4842 <function>assert</function> in your code.
4846 GHC ignores assertions when optimisation is turned on with the
4847 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4848 <literal>assert pred e</literal> will be rewritten to
4849 <literal>e</literal>. You can also disable assertions using the
4850 <option>-fignore-asserts</option>
4851 option<indexterm><primary><option>-fignore-asserts</option></primary>
4852 </indexterm>.</para>
4855 Assertion failures can be caught, see the documentation for the
4856 <literal>Control.Exception</literal> library for the details.
4862 <!-- =============================== PRAGMAS =========================== -->
4864 <sect1 id="pragmas">
4865 <title>Pragmas</title>
4867 <indexterm><primary>pragma</primary></indexterm>
4869 <para>GHC supports several pragmas, or instructions to the
4870 compiler placed in the source code. Pragmas don't normally affect
4871 the meaning of the program, but they might affect the efficiency
4872 of the generated code.</para>
4874 <para>Pragmas all take the form
4876 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4878 where <replaceable>word</replaceable> indicates the type of
4879 pragma, and is followed optionally by information specific to that
4880 type of pragma. Case is ignored in
4881 <replaceable>word</replaceable>. The various values for
4882 <replaceable>word</replaceable> that GHC understands are described
4883 in the following sections; any pragma encountered with an
4884 unrecognised <replaceable>word</replaceable> is (silently)
4887 <sect2 id="deprecated-pragma">
4888 <title>DEPRECATED pragma</title>
4889 <indexterm><primary>DEPRECATED</primary>
4892 <para>The DEPRECATED pragma lets you specify that a particular
4893 function, class, or type, is deprecated. There are two
4898 <para>You can deprecate an entire module thus:</para>
4900 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4903 <para>When you compile any module that import
4904 <literal>Wibble</literal>, GHC will print the specified
4909 <para>You can deprecate a function, class, type, or data constructor, with the
4910 following top-level declaration:</para>
4912 {-# DEPRECATED f, C, T "Don't use these" #-}
4914 <para>When you compile any module that imports and uses any
4915 of the specified entities, GHC will print the specified
4917 <para> You can only depecate entities declared at top level in the module
4918 being compiled, and you can only use unqualified names in the list of
4919 entities being deprecated. A capitalised name, such as <literal>T</literal>
4920 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4921 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4922 both are in scope. If both are in scope, there is currently no way to deprecate
4923 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4926 Any use of the deprecated item, or of anything from a deprecated
4927 module, will be flagged with an appropriate message. However,
4928 deprecations are not reported for
4929 (a) uses of a deprecated function within its defining module, and
4930 (b) uses of a deprecated function in an export list.
4931 The latter reduces spurious complaints within a library
4932 in which one module gathers together and re-exports
4933 the exports of several others.
4935 <para>You can suppress the warnings with the flag
4936 <option>-fno-warn-deprecations</option>.</para>
4939 <sect2 id="include-pragma">
4940 <title>INCLUDE pragma</title>
4942 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4943 of C header files that should be <literal>#include</literal>'d into
4944 the C source code generated by the compiler for the current module (if
4945 compiling via C). For example:</para>
4948 {-# INCLUDE "foo.h" #-}
4949 {-# INCLUDE <stdio.h> #-}</programlisting>
4951 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4952 your source file with any <literal>OPTIONS_GHC</literal>
4955 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4956 to the <option>-#include</option> option (<xref
4957 linkend="options-C-compiler" />), because the
4958 <literal>INCLUDE</literal> pragma is understood by other
4959 compilers. Yet another alternative is to add the include file to each
4960 <literal>foreign import</literal> declaration in your code, but we
4961 don't recommend using this approach with GHC.</para>
4964 <sect2 id="inline-noinline-pragma">
4965 <title>INLINE and NOINLINE pragmas</title>
4967 <para>These pragmas control the inlining of function
4970 <sect3 id="inline-pragma">
4971 <title>INLINE pragma</title>
4972 <indexterm><primary>INLINE</primary></indexterm>
4974 <para>GHC (with <option>-O</option>, as always) tries to
4975 inline (or “unfold”) functions/values that are
4976 “small enough,” thus avoiding the call overhead
4977 and possibly exposing other more-wonderful optimisations.
4978 Normally, if GHC decides a function is “too
4979 expensive” to inline, it will not do so, nor will it
4980 export that unfolding for other modules to use.</para>
4982 <para>The sledgehammer you can bring to bear is the
4983 <literal>INLINE</literal><indexterm><primary>INLINE
4984 pragma</primary></indexterm> pragma, used thusly:</para>
4987 key_function :: Int -> String -> (Bool, Double)
4989 #ifdef __GLASGOW_HASKELL__
4990 {-# INLINE key_function #-}
4994 <para>(You don't need to do the C pre-processor carry-on
4995 unless you're going to stick the code through HBC—it
4996 doesn't like <literal>INLINE</literal> pragmas.)</para>
4998 <para>The major effect of an <literal>INLINE</literal> pragma
4999 is to declare a function's “cost” to be very low.
5000 The normal unfolding machinery will then be very keen to
5003 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5004 function can be put anywhere its type signature could be
5007 <para><literal>INLINE</literal> pragmas are a particularly
5009 <literal>then</literal>/<literal>return</literal> (or
5010 <literal>bind</literal>/<literal>unit</literal>) functions in
5011 a monad. For example, in GHC's own
5012 <literal>UniqueSupply</literal> monad code, we have:</para>
5015 #ifdef __GLASGOW_HASKELL__
5016 {-# INLINE thenUs #-}
5017 {-# INLINE returnUs #-}
5021 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5022 linkend="noinline-pragma"/>).</para>
5025 <sect3 id="noinline-pragma">
5026 <title>NOINLINE pragma</title>
5028 <indexterm><primary>NOINLINE</primary></indexterm>
5029 <indexterm><primary>NOTINLINE</primary></indexterm>
5031 <para>The <literal>NOINLINE</literal> pragma does exactly what
5032 you'd expect: it stops the named function from being inlined
5033 by the compiler. You shouldn't ever need to do this, unless
5034 you're very cautious about code size.</para>
5036 <para><literal>NOTINLINE</literal> is a synonym for
5037 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5038 specified by Haskell 98 as the standard way to disable
5039 inlining, so it should be used if you want your code to be
5043 <sect3 id="phase-control">
5044 <title>Phase control</title>
5046 <para> Sometimes you want to control exactly when in GHC's
5047 pipeline the INLINE pragma is switched on. Inlining happens
5048 only during runs of the <emphasis>simplifier</emphasis>. Each
5049 run of the simplifier has a different <emphasis>phase
5050 number</emphasis>; the phase number decreases towards zero.
5051 If you use <option>-dverbose-core2core</option> you'll see the
5052 sequence of phase numbers for successive runs of the
5053 simplifier. In an INLINE pragma you can optionally specify a
5057 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5058 <literal>f</literal>
5059 until phase <literal>k</literal>, but from phase
5060 <literal>k</literal> onwards be very keen to inline it.
5063 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5064 <literal>f</literal>
5065 until phase <literal>k</literal>, but from phase
5066 <literal>k</literal> onwards do not inline it.
5069 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5070 <literal>f</literal>
5071 until phase <literal>k</literal>, but from phase
5072 <literal>k</literal> onwards be willing to inline it (as if
5073 there was no pragma).
5076 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5077 <literal>f</literal>
5078 until phase <literal>k</literal>, but from phase
5079 <literal>k</literal> onwards do not inline it.
5082 The same information is summarised here:
5084 -- Before phase 2 Phase 2 and later
5085 {-# INLINE [2] f #-} -- No Yes
5086 {-# INLINE [~2] f #-} -- Yes No
5087 {-# NOINLINE [2] f #-} -- No Maybe
5088 {-# NOINLINE [~2] f #-} -- Maybe No
5090 {-# INLINE f #-} -- Yes Yes
5091 {-# NOINLINE f #-} -- No No
5093 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5094 function body is small, or it is applied to interesting-looking arguments etc).
5095 Another way to understand the semantics is this:
5097 <listitem><para>For both INLINE and NOINLINE, the phase number says
5098 when inlining is allowed at all.</para></listitem>
5099 <listitem><para>The INLINE pragma has the additional effect of making the
5100 function body look small, so that when inlining is allowed it is very likely to
5105 <para>The same phase-numbering control is available for RULES
5106 (<xref linkend="rewrite-rules"/>).</para>
5110 <sect2 id="language-pragma">
5111 <title>LANGUAGE pragma</title>
5113 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5114 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5116 <para>This allows language extensions to be enabled in a portable way.
5117 It is the intention that all Haskell compilers support the
5118 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5119 all extensions are supported by all compilers, of
5120 course. The <literal>LANGUAGE</literal> pragma should be used instead
5121 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5123 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5125 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5127 <para>Any extension from the <literal>Extension</literal> type defined in
5129 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>
5133 <sect2 id="line-pragma">
5134 <title>LINE pragma</title>
5136 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5137 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5138 <para>This pragma is similar to C's <literal>#line</literal>
5139 pragma, and is mainly for use in automatically generated Haskell
5140 code. It lets you specify the line number and filename of the
5141 original code; for example</para>
5143 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5145 <para>if you'd generated the current file from something called
5146 <filename>Foo.vhs</filename> and this line corresponds to line
5147 42 in the original. GHC will adjust its error messages to refer
5148 to the line/file named in the <literal>LINE</literal>
5152 <sect2 id="options-pragma">
5153 <title>OPTIONS_GHC pragma</title>
5154 <indexterm><primary>OPTIONS_GHC</primary>
5156 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5159 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5160 additional options that are given to the compiler when compiling
5161 this source file. See <xref linkend="source-file-options"/> for
5164 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5165 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5169 <title>RULES pragma</title>
5171 <para>The RULES pragma lets you specify rewrite rules. It is
5172 described in <xref linkend="rewrite-rules"/>.</para>
5175 <sect2 id="specialize-pragma">
5176 <title>SPECIALIZE pragma</title>
5178 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5179 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5180 <indexterm><primary>overloading, death to</primary></indexterm>
5182 <para>(UK spelling also accepted.) For key overloaded
5183 functions, you can create extra versions (NB: more code space)
5184 specialised to particular types. Thus, if you have an
5185 overloaded function:</para>
5188 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5191 <para>If it is heavily used on lists with
5192 <literal>Widget</literal> keys, you could specialise it as
5196 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5199 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5200 be put anywhere its type signature could be put.</para>
5202 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5203 (a) a specialised version of the function and (b) a rewrite rule
5204 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5205 un-specialised function into a call to the specialised one.</para>
5207 <para>The type in a SPECIALIZE pragma can be any type that is less
5208 polymorphic than the type of the original function. In concrete terms,
5209 if the original function is <literal>f</literal> then the pragma
5211 {-# SPECIALIZE f :: <type> #-}
5213 is valid if and only if the defintion
5215 f_spec :: <type>
5218 is valid. Here are some examples (where we only give the type signature
5219 for the original function, not its code):
5221 f :: Eq a => a -> b -> b
5222 {-# SPECIALISE f :: Int -> b -> b #-}
5224 g :: (Eq a, Ix b) => a -> b -> b
5225 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5227 h :: Eq a => a -> a -> a
5228 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5230 The last of these examples will generate a
5231 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5232 well. If you use this kind of specialisation, let us know how well it works.
5235 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5236 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5237 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5238 The <literal>INLINE</literal> pragma affects the specialised verison of the
5239 function (only), and applies even if the function is recursive. The motivating
5242 -- A GADT for arrays with type-indexed representation
5244 ArrInt :: !Int -> ByteArray# -> Arr Int
5245 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5247 (!:) :: Arr e -> Int -> e
5248 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5249 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5250 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5251 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5253 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5254 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5255 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5256 the specialised function will be inlined. It has two calls to
5257 <literal>(!:)</literal>,
5258 both at type <literal>Int</literal>. Both these calls fire the first
5259 specialisation, whose body is also inlined. The result is a type-based
5260 unrolling of the indexing function.</para>
5261 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5262 on an ordinarily-recursive function.</para>
5264 <para>Note: In earlier versions of GHC, it was possible to provide your own
5265 specialised function for a given type:
5268 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5271 This feature has been removed, as it is now subsumed by the
5272 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5276 <sect2 id="specialize-instance-pragma">
5277 <title>SPECIALIZE instance pragma
5281 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5282 <indexterm><primary>overloading, death to</primary></indexterm>
5283 Same idea, except for instance declarations. For example:
5286 instance (Eq a) => Eq (Foo a) where {
5287 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5291 The pragma must occur inside the <literal>where</literal> part
5292 of the instance declaration.
5295 Compatible with HBC, by the way, except perhaps in the placement
5301 <sect2 id="unpack-pragma">
5302 <title>UNPACK pragma</title>
5304 <indexterm><primary>UNPACK</primary></indexterm>
5306 <para>The <literal>UNPACK</literal> indicates to the compiler
5307 that it should unpack the contents of a constructor field into
5308 the constructor itself, removing a level of indirection. For
5312 data T = T {-# UNPACK #-} !Float
5313 {-# UNPACK #-} !Float
5316 <para>will create a constructor <literal>T</literal> containing
5317 two unboxed floats. This may not always be an optimisation: if
5318 the <function>T</function> constructor is scrutinised and the
5319 floats passed to a non-strict function for example, they will
5320 have to be reboxed (this is done automatically by the
5323 <para>Unpacking constructor fields should only be used in
5324 conjunction with <option>-O</option>, in order to expose
5325 unfoldings to the compiler so the reboxing can be removed as
5326 often as possible. For example:</para>
5330 f (T f1 f2) = f1 + f2
5333 <para>The compiler will avoid reboxing <function>f1</function>
5334 and <function>f2</function> by inlining <function>+</function>
5335 on floats, but only when <option>-O</option> is on.</para>
5337 <para>Any single-constructor data is eligible for unpacking; for
5341 data T = T {-# UNPACK #-} !(Int,Int)
5344 <para>will store the two <literal>Int</literal>s directly in the
5345 <function>T</function> constructor, by flattening the pair.
5346 Multi-level unpacking is also supported:</para>
5349 data T = T {-# UNPACK #-} !S
5350 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5353 <para>will store two unboxed <literal>Int#</literal>s
5354 directly in the <function>T</function> constructor. The
5355 unpacker can see through newtypes, too.</para>
5357 <para>If a field cannot be unpacked, you will not get a warning,
5358 so it might be an idea to check the generated code with
5359 <option>-ddump-simpl</option>.</para>
5361 <para>See also the <option>-funbox-strict-fields</option> flag,
5362 which essentially has the effect of adding
5363 <literal>{-# UNPACK #-}</literal> to every strict
5364 constructor field.</para>
5369 <!-- ======================= REWRITE RULES ======================== -->
5371 <sect1 id="rewrite-rules">
5372 <title>Rewrite rules
5374 <indexterm><primary>RULES pragma</primary></indexterm>
5375 <indexterm><primary>pragma, RULES</primary></indexterm>
5376 <indexterm><primary>rewrite rules</primary></indexterm></title>
5379 The programmer can specify rewrite rules as part of the source program
5380 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5381 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5382 and (b) the <option>-frules-off</option> flag
5383 (<xref linkend="options-f"/>) is not specified, and (c) the
5384 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5393 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5400 <title>Syntax</title>
5403 From a syntactic point of view:
5409 There may be zero or more rules in a <literal>RULES</literal> pragma.
5416 Each rule has a name, enclosed in double quotes. The name itself has
5417 no significance at all. It is only used when reporting how many times the rule fired.
5423 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5424 immediately after the name of the rule. Thus:
5427 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5430 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5431 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5440 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5441 is set, so you must lay out your rules starting in the same column as the
5442 enclosing definitions.
5449 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5450 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5451 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5452 by spaces, just like in a type <literal>forall</literal>.
5458 A pattern variable may optionally have a type signature.
5459 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5460 For example, here is the <literal>foldr/build</literal> rule:
5463 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5464 foldr k z (build g) = g k z
5467 Since <function>g</function> has a polymorphic type, it must have a type signature.
5474 The left hand side of a rule must consist of a top-level variable applied
5475 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5478 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5479 "wrong2" forall f. f True = True
5482 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5489 A rule does not need to be in the same module as (any of) the
5490 variables it mentions, though of course they need to be in scope.
5496 Rules are automatically exported from a module, just as instance declarations are.
5507 <title>Semantics</title>
5510 From a semantic point of view:
5516 Rules are only applied if you use the <option>-O</option> flag.
5522 Rules are regarded as left-to-right rewrite rules.
5523 When GHC finds an expression that is a substitution instance of the LHS
5524 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5525 By "a substitution instance" we mean that the LHS can be made equal to the
5526 expression by substituting for the pattern variables.
5533 The LHS and RHS of a rule are typechecked, and must have the
5541 GHC makes absolutely no attempt to verify that the LHS and RHS
5542 of a rule have the same meaning. That is undecidable in general, and
5543 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5550 GHC makes no attempt to make sure that the rules are confluent or
5551 terminating. For example:
5554 "loop" forall x,y. f x y = f y x
5557 This rule will cause the compiler to go into an infinite loop.
5564 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5570 GHC currently uses a very simple, syntactic, matching algorithm
5571 for matching a rule LHS with an expression. It seeks a substitution
5572 which makes the LHS and expression syntactically equal modulo alpha
5573 conversion. The pattern (rule), but not the expression, is eta-expanded if
5574 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5575 But not beta conversion (that's called higher-order matching).
5579 Matching is carried out on GHC's intermediate language, which includes
5580 type abstractions and applications. So a rule only matches if the
5581 types match too. See <xref linkend="rule-spec"/> below.
5587 GHC keeps trying to apply the rules as it optimises the program.
5588 For example, consider:
5597 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5598 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5599 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5600 not be substituted, and the rule would not fire.
5607 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5608 that appears on the LHS of a rule</emphasis>, because once you have substituted
5609 for something you can't match against it (given the simple minded
5610 matching). So if you write the rule
5613 "map/map" forall f,g. map f . map g = map (f.g)
5616 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5617 It will only match something written with explicit use of ".".
5618 Well, not quite. It <emphasis>will</emphasis> match the expression
5624 where <function>wibble</function> is defined:
5627 wibble f g = map f . map g
5630 because <function>wibble</function> will be inlined (it's small).
5632 Later on in compilation, GHC starts inlining even things on the
5633 LHS of rules, but still leaves the rules enabled. This inlining
5634 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5641 All rules are implicitly exported from the module, and are therefore
5642 in force in any module that imports the module that defined the rule, directly
5643 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5644 in force when compiling A.) The situation is very similar to that for instance
5656 <title>List fusion</title>
5659 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5660 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5661 intermediate list should be eliminated entirely.
5665 The following are good producers:
5677 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5683 Explicit lists (e.g. <literal>[True, False]</literal>)
5689 The cons constructor (e.g <literal>3:4:[]</literal>)
5695 <function>++</function>
5701 <function>map</function>
5707 <function>take</function>, <function>filter</function>
5713 <function>iterate</function>, <function>repeat</function>
5719 <function>zip</function>, <function>zipWith</function>
5728 The following are good consumers:
5740 <function>array</function> (on its second argument)
5746 <function>length</function>
5752 <function>++</function> (on its first argument)
5758 <function>foldr</function>
5764 <function>map</function>
5770 <function>take</function>, <function>filter</function>
5776 <function>concat</function>
5782 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5788 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5789 will fuse with one but not the other)
5795 <function>partition</function>
5801 <function>head</function>
5807 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5813 <function>sequence_</function>
5819 <function>msum</function>
5825 <function>sortBy</function>
5834 So, for example, the following should generate no intermediate lists:
5837 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5843 This list could readily be extended; if there are Prelude functions that you use
5844 a lot which are not included, please tell us.
5848 If you want to write your own good consumers or producers, look at the
5849 Prelude definitions of the above functions to see how to do so.
5854 <sect2 id="rule-spec">
5855 <title>Specialisation
5859 Rewrite rules can be used to get the same effect as a feature
5860 present in earlier versions of GHC.
5861 For example, suppose that:
5864 genericLookup :: Ord a => Table a b -> a -> b
5865 intLookup :: Table Int b -> Int -> b
5868 where <function>intLookup</function> is an implementation of
5869 <function>genericLookup</function> that works very fast for
5870 keys of type <literal>Int</literal>. You might wish
5871 to tell GHC to use <function>intLookup</function> instead of
5872 <function>genericLookup</function> whenever the latter was called with
5873 type <literal>Table Int b -> Int -> b</literal>.
5874 It used to be possible to write
5877 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5880 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5883 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5886 This slightly odd-looking rule instructs GHC to replace
5887 <function>genericLookup</function> by <function>intLookup</function>
5888 <emphasis>whenever the types match</emphasis>.
5889 What is more, this rule does not need to be in the same
5890 file as <function>genericLookup</function>, unlike the
5891 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5892 have an original definition available to specialise).
5895 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5896 <function>intLookup</function> really behaves as a specialised version
5897 of <function>genericLookup</function>!!!</para>
5899 <para>An example in which using <literal>RULES</literal> for
5900 specialisation will Win Big:
5903 toDouble :: Real a => a -> Double
5904 toDouble = fromRational . toRational
5906 {-# RULES "toDouble/Int" toDouble = i2d #-}
5907 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5910 The <function>i2d</function> function is virtually one machine
5911 instruction; the default conversion—via an intermediate
5912 <literal>Rational</literal>—is obscenely expensive by
5919 <title>Controlling what's going on</title>
5927 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5933 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5934 If you add <option>-dppr-debug</option> you get a more detailed listing.
5940 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5943 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5944 {-# INLINE build #-}
5948 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5949 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5950 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5951 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5958 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5959 see how to write rules that will do fusion and yet give an efficient
5960 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5970 <sect2 id="core-pragma">
5971 <title>CORE pragma</title>
5973 <indexterm><primary>CORE pragma</primary></indexterm>
5974 <indexterm><primary>pragma, CORE</primary></indexterm>
5975 <indexterm><primary>core, annotation</primary></indexterm>
5978 The external core format supports <quote>Note</quote> annotations;
5979 the <literal>CORE</literal> pragma gives a way to specify what these
5980 should be in your Haskell source code. Syntactically, core
5981 annotations are attached to expressions and take a Haskell string
5982 literal as an argument. The following function definition shows an
5986 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5989 Semantically, this is equivalent to:
5997 However, when external for is generated (via
5998 <option>-fext-core</option>), there will be Notes attached to the
5999 expressions <function>show</function> and <varname>x</varname>.
6000 The core function declaration for <function>f</function> is:
6004 f :: %forall a . GHCziShow.ZCTShow a ->
6005 a -> GHCziBase.ZMZN GHCziBase.Char =
6006 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6008 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6010 (tpl1::GHCziBase.Int ->
6012 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6014 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6015 (tpl3::GHCziBase.ZMZN a ->
6016 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6024 Here, we can see that the function <function>show</function> (which
6025 has been expanded out to a case expression over the Show dictionary)
6026 has a <literal>%note</literal> attached to it, as does the
6027 expression <varname>eta</varname> (which used to be called
6028 <varname>x</varname>).
6035 <sect1 id="special-ids">
6036 <title>Special built-in functions</title>
6037 <para>GHC has a few built-in funcions with special behaviour,
6038 described in this section. All are exported by
6039 <literal>GHC.Exts</literal>.</para>
6041 <sect2> <title>The <literal>inline</literal> function </title>
6043 The <literal>inline</literal> function is somewhat experimental.
6047 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6048 is inlined, regardless of its size. More precisely, the call
6049 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6051 This allows the programmer to control inlining from
6052 a particular <emphasis>call site</emphasis>
6053 rather than the <emphasis>definition site</emphasis> of the function
6054 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6057 This inlining occurs regardless of the argument to the call
6058 or the size of <literal>f</literal>'s definition; it is unconditional.
6059 The main caveat is that <literal>f</literal>'s definition must be
6060 visible to the compiler. That is, <literal>f</literal> must be
6061 let-bound in the current scope.
6062 If no inlining takes place, the <literal>inline</literal> function
6063 expands to the identity function in Phase zero; so its use imposes
6066 <para> If the function is defined in another
6067 module, GHC only exposes its inlining in the interface file if the
6068 function is sufficiently small that it <emphasis>might</emphasis> be
6069 inlined by the automatic mechanism. There is currently no way to tell
6070 GHC to expose arbitrarily-large functions in the interface file. (This
6071 shortcoming is something that could be fixed, with some kind of pragma.)
6075 <sect2> <title>The <literal>inline</literal> function </title>
6077 The <literal>lazy</literal> function restrains strictness analysis a little:
6081 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6082 but <literal>lazy</literal> has a magical property so far as strictness
6083 analysis is concerned: it is lazy in its first argument,
6084 even though its semantics is strict. After strictness analysis has run,
6085 calls to <literal>lazy</literal> are inlined to be the identity function.
6088 This behaviour is occasionally useful when controlling evaluation order.
6089 Notably, <literal>lazy</literal> is used in the library definition of
6090 <literal>Control.Parallel.par</literal>:
6093 par x y = case (par# x) of { _ -> lazy y }
6095 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6096 look strict in <literal>y</literal> which would defeat the whole
6097 purpose of <literal>par</literal>.
6103 <sect1 id="generic-classes">
6104 <title>Generic classes</title>
6106 <para>(Note: support for generic classes is currently broken in
6110 The ideas behind this extension are described in detail in "Derivable type classes",
6111 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6112 An example will give the idea:
6120 fromBin :: [Int] -> (a, [Int])
6122 toBin {| Unit |} Unit = []
6123 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6124 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6125 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6127 fromBin {| Unit |} bs = (Unit, bs)
6128 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6129 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6130 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6131 (y,bs'') = fromBin bs'
6134 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6135 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6136 which are defined thus in the library module <literal>Generics</literal>:
6140 data a :+: b = Inl a | Inr b
6141 data a :*: b = a :*: b
6144 Now you can make a data type into an instance of Bin like this:
6146 instance (Bin a, Bin b) => Bin (a,b)
6147 instance Bin a => Bin [a]
6149 That is, just leave off the "where" clause. Of course, you can put in the
6150 where clause and over-ride whichever methods you please.
6154 <title> Using generics </title>
6155 <para>To use generics you need to</para>
6158 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6159 <option>-fgenerics</option> (to generate extra per-data-type code),
6160 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6164 <para>Import the module <literal>Generics</literal> from the
6165 <literal>lang</literal> package. This import brings into
6166 scope the data types <literal>Unit</literal>,
6167 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6168 don't need this import if you don't mention these types
6169 explicitly; for example, if you are simply giving instance
6170 declarations.)</para>
6175 <sect2> <title> Changes wrt the paper </title>
6177 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6178 can be written infix (indeed, you can now use
6179 any operator starting in a colon as an infix type constructor). Also note that
6180 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6181 Finally, note that the syntax of the type patterns in the class declaration
6182 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6183 alone would ambiguous when they appear on right hand sides (an extension we
6184 anticipate wanting).
6188 <sect2> <title>Terminology and restrictions</title>
6190 Terminology. A "generic default method" in a class declaration
6191 is one that is defined using type patterns as above.
6192 A "polymorphic default method" is a default method defined as in Haskell 98.
6193 A "generic class declaration" is a class declaration with at least one
6194 generic default method.
6202 Alas, we do not yet implement the stuff about constructor names and
6209 A generic class can have only one parameter; you can't have a generic
6210 multi-parameter class.
6216 A default method must be defined entirely using type patterns, or entirely
6217 without. So this is illegal:
6220 op :: a -> (a, Bool)
6221 op {| Unit |} Unit = (Unit, True)
6224 However it is perfectly OK for some methods of a generic class to have
6225 generic default methods and others to have polymorphic default methods.
6231 The type variable(s) in the type pattern for a generic method declaration
6232 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:
6236 op {| p :*: q |} (x :*: y) = op (x :: p)
6244 The type patterns in a generic default method must take one of the forms:
6250 where "a" and "b" are type variables. Furthermore, all the type patterns for
6251 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6252 must use the same type variables. So this is illegal:
6256 op {| a :+: b |} (Inl x) = True
6257 op {| p :+: q |} (Inr y) = False
6259 The type patterns must be identical, even in equations for different methods of the class.
6260 So this too is illegal:
6264 op1 {| a :*: b |} (x :*: y) = True
6267 op2 {| p :*: q |} (x :*: y) = False
6269 (The reason for this restriction is that we gather all the equations for a particular type consructor
6270 into a single generic instance declaration.)
6276 A generic method declaration must give a case for each of the three type constructors.
6282 The type for a generic method can be built only from:
6284 <listitem> <para> Function arrows </para> </listitem>
6285 <listitem> <para> Type variables </para> </listitem>
6286 <listitem> <para> Tuples </para> </listitem>
6287 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6289 Here are some example type signatures for generic methods:
6292 op2 :: Bool -> (a,Bool)
6293 op3 :: [Int] -> a -> a
6296 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6300 This restriction is an implementation restriction: we just havn't got around to
6301 implementing the necessary bidirectional maps over arbitrary type constructors.
6302 It would be relatively easy to add specific type constructors, such as Maybe and list,
6303 to the ones that are allowed.</para>
6308 In an instance declaration for a generic class, the idea is that the compiler
6309 will fill in the methods for you, based on the generic templates. However it can only
6314 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6319 No constructor of the instance type has unboxed fields.
6323 (Of course, these things can only arise if you are already using GHC extensions.)
6324 However, you can still give an instance declarations for types which break these rules,
6325 provided you give explicit code to override any generic default methods.
6333 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6334 what the compiler does with generic declarations.
6339 <sect2> <title> Another example </title>
6341 Just to finish with, here's another example I rather like:
6345 nCons {| Unit |} _ = 1
6346 nCons {| a :*: b |} _ = 1
6347 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6350 tag {| Unit |} _ = 1
6351 tag {| a :*: b |} _ = 1
6352 tag {| a :+: b |} (Inl x) = tag x
6353 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6362 ;;; Local Variables: ***
6364 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
projects / ghc-hetmet.git / blob