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.</para>
111 <para>New reserved words: <literal>foreign</literal>.</para>
117 <option>-fno-monomorphism-restriction</option>,<option>-fno-mono-pat-binds</option>:
120 <para> These two flags control how generalisation is done.
121 See <xref linkend="monomorphism"/>.
128 <option>-fextended-default-rules</option>:
129 <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
132 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
133 Independent of the <option>-fglasgow-exts</option>
140 <option>-fallow-overlapping-instances</option>
141 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
144 <option>-fallow-undecidable-instances</option>
145 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
148 <option>-fallow-incoherent-instances</option>
149 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
152 <option>-fcontext-stack=N</option>
153 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
156 <para> See <xref linkend="instance-decls"/>. Only relevant
157 if you also use <option>-fglasgow-exts</option>.</para>
163 <option>-finline-phase</option>
164 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
167 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
168 you also use <option>-fglasgow-exts</option>.</para>
174 <option>-farrows</option>
175 <indexterm><primary><option>-farrows</option></primary></indexterm>
178 <para>See <xref linkend="arrow-notation"/>. Independent of
179 <option>-fglasgow-exts</option>.</para>
181 <para>New reserved words/symbols: <literal>rec</literal>,
182 <literal>proc</literal>, <literal>-<</literal>,
183 <literal>>-</literal>, <literal>-<<</literal>,
184 <literal>>>-</literal>.</para>
186 <para>Other syntax stolen: <literal>(|</literal>,
187 <literal>|)</literal>.</para>
193 <option>-fgenerics</option>
194 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
197 <para>See <xref linkend="generic-classes"/>. Independent of
198 <option>-fglasgow-exts</option>.</para>
203 <term><option>-fno-implicit-prelude</option></term>
205 <para><indexterm><primary>-fno-implicit-prelude
206 option</primary></indexterm> GHC normally imports
207 <filename>Prelude.hi</filename> files for you. If you'd
208 rather it didn't, then give it a
209 <option>-fno-implicit-prelude</option> option. The idea is
210 that you can then import a Prelude of your own. (But don't
211 call it <literal>Prelude</literal>; the Haskell module
212 namespace is flat, and you must not conflict with any
213 Prelude module.)</para>
215 <para>Even though you have not imported the Prelude, most of
216 the built-in syntax still refers to the built-in Haskell
217 Prelude types and values, as specified by the Haskell
218 Report. For example, the type <literal>[Int]</literal>
219 still means <literal>Prelude.[] Int</literal>; tuples
220 continue to refer to the standard Prelude tuples; the
221 translation for list comprehensions continues to use
222 <literal>Prelude.map</literal> etc.</para>
224 <para>However, <option>-fno-implicit-prelude</option> does
225 change the handling of certain built-in syntax: see <xref
226 linkend="rebindable-syntax"/>.</para>
231 <term><option>-fimplicit-params</option></term>
233 <para>Enables implicit parameters (see <xref
234 linkend="implicit-parameters"/>). Currently also implied by
235 <option>-fglasgow-exts</option>.</para>
238 <literal>?<replaceable>varid</replaceable></literal>,
239 <literal>%<replaceable>varid</replaceable></literal>.</para>
244 <term><option>-foverloaded-strings</option></term>
246 <para>Enables overloaded string literals (see <xref
247 linkend="overloaded-strings"/>).</para>
252 <term><option>-fscoped-type-variables</option></term>
254 <para>Enables lexically-scoped type variables (see <xref
255 linkend="scoped-type-variables"/>). Implied by
256 <option>-fglasgow-exts</option>.</para>
261 <term><option>-fth</option></term>
263 <para>Enables Template Haskell (see <xref
264 linkend="template-haskell"/>). This flag must
265 be given explicitly; it is no longer implied by
266 <option>-fglasgow-exts</option>.</para>
268 <para>Syntax stolen: <literal>[|</literal>,
269 <literal>[e|</literal>, <literal>[p|</literal>,
270 <literal>[d|</literal>, <literal>[t|</literal>,
271 <literal>$(</literal>,
272 <literal>$<replaceable>varid</replaceable></literal>.</para>
279 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
280 <sect1 id="primitives">
281 <title>Unboxed types and primitive operations</title>
283 <para>GHC is built on a raft of primitive data types and operations.
284 While you really can use this stuff to write fast code,
285 we generally find it a lot less painful, and more satisfying in the
286 long run, to use higher-level language features and libraries. With
287 any luck, the code you write will be optimised to the efficient
288 unboxed version in any case. And if it isn't, we'd like to know
291 <para>We do not currently have good, up-to-date documentation about the
292 primitives, perhaps because they are mainly intended for internal use.
293 There used to be a long section about them here in the User Guide, but it
294 became out of date, and wrong information is worse than none.</para>
296 <para>The Real Truth about what primitive types there are, and what operations
297 work over those types, is held in the file
298 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
299 This file is used directly to generate GHC's primitive-operation definitions, so
300 it is always correct! It is also intended for processing into text.</para>
303 the result of such processing is part of the description of the
305 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
306 Core language</ulink>.
307 So that document is a good place to look for a type-set version.
308 We would be very happy if someone wanted to volunteer to produce an SGML
309 back end to the program that processes <filename>primops.txt</filename> so that
310 we could include the results here in the User Guide.</para>
312 <para>What follows here is a brief summary of some main points.</para>
314 <sect2 id="glasgow-unboxed">
319 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
322 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
323 that values of that type are represented by a pointer to a heap
324 object. The representation of a Haskell <literal>Int</literal>, for
325 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
326 type, however, is represented by the value itself, no pointers or heap
327 allocation are involved.
331 Unboxed types correspond to the “raw machine” types you
332 would use in C: <literal>Int#</literal> (long int),
333 <literal>Double#</literal> (double), <literal>Addr#</literal>
334 (void *), etc. The <emphasis>primitive operations</emphasis>
335 (PrimOps) on these types are what you might expect; e.g.,
336 <literal>(+#)</literal> is addition on
337 <literal>Int#</literal>s, and is the machine-addition that we all
338 know and love—usually one instruction.
342 Primitive (unboxed) types cannot be defined in Haskell, and are
343 therefore built into the language and compiler. Primitive types are
344 always unlifted; that is, a value of a primitive type cannot be
345 bottom. We use the convention that primitive types, values, and
346 operations have a <literal>#</literal> suffix.
350 Primitive values are often represented by a simple bit-pattern, such
351 as <literal>Int#</literal>, <literal>Float#</literal>,
352 <literal>Double#</literal>. But this is not necessarily the case:
353 a primitive value might be represented by a pointer to a
354 heap-allocated object. Examples include
355 <literal>Array#</literal>, the type of primitive arrays. A
356 primitive array is heap-allocated because it is too big a value to fit
357 in a register, and would be too expensive to copy around; in a sense,
358 it is accidental that it is represented by a pointer. If a pointer
359 represents a primitive value, then it really does point to that value:
360 no unevaluated thunks, no indirections…nothing can be at the
361 other end of the pointer than the primitive value.
362 A numerically-intensive program using unboxed types can
363 go a <emphasis>lot</emphasis> faster than its “standard”
364 counterpart—we saw a threefold speedup on one example.
368 There are some restrictions on the use of primitive types:
370 <listitem><para>The main restriction
371 is that you can't pass a primitive value to a polymorphic
372 function or store one in a polymorphic data type. This rules out
373 things like <literal>[Int#]</literal> (i.e. lists of primitive
374 integers). The reason for this restriction is that polymorphic
375 arguments and constructor fields are assumed to be pointers: if an
376 unboxed integer is stored in one of these, the garbage collector would
377 attempt to follow it, leading to unpredictable space leaks. Or a
378 <function>seq</function> operation on the polymorphic component may
379 attempt to dereference the pointer, with disastrous results. Even
380 worse, the unboxed value might be larger than a pointer
381 (<literal>Double#</literal> for instance).
384 <listitem><para> You cannot bind a variable with an unboxed type
385 in a <emphasis>top-level</emphasis> binding.
387 <listitem><para> You cannot bind a variable with an unboxed type
388 in a <emphasis>recursive</emphasis> binding.
390 <listitem><para> You may bind unboxed variables in a (non-recursive,
391 non-top-level) pattern binding, but any such variable causes the entire
393 to become strict. For example:
395 data Foo = Foo Int Int#
397 f x = let (Foo a b, w) = ..rhs.. in ..body..
399 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
401 is strict, and the program behaves as if you had written
403 data Foo = Foo Int Int#
405 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
414 <sect2 id="unboxed-tuples">
415 <title>Unboxed Tuples
419 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
420 they're available by default with <option>-fglasgow-exts</option>. An
421 unboxed tuple looks like this:
433 where <literal>e_1..e_n</literal> are expressions of any
434 type (primitive or non-primitive). The type of an unboxed tuple looks
439 Unboxed tuples are used for functions that need to return multiple
440 values, but they avoid the heap allocation normally associated with
441 using fully-fledged tuples. When an unboxed tuple is returned, the
442 components are put directly into registers or on the stack; the
443 unboxed tuple itself does not have a composite representation. Many
444 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
446 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
447 tuples to avoid unnecessary allocation during sequences of operations.
451 There are some pretty stringent restrictions on the use of unboxed tuples:
456 Values of unboxed tuple types are subject to the same restrictions as
457 other unboxed types; i.e. they may not be stored in polymorphic data
458 structures or passed to polymorphic functions.
465 No variable can have an unboxed tuple type, nor may a constructor or function
466 argument have an unboxed tuple type. The following are all illegal:
470 data Foo = Foo (# Int, Int #)
472 f :: (# Int, Int #) -> (# Int, Int #)
475 g :: (# Int, Int #) -> Int
478 h x = let y = (# x,x #) in ...
485 The typical use of unboxed tuples is simply to return multiple values,
486 binding those multiple results with a <literal>case</literal> expression, thus:
488 f x y = (# x+1, y-1 #)
489 g x = case f x x of { (# a, b #) -> a + b }
491 You can have an unboxed tuple in a pattern binding, thus
493 f x = let (# p,q #) = h x in ..body..
495 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
496 the resulting binding is lazy like any other Haskell pattern binding. The
497 above example desugars like this:
499 f x = let t = case h x o f{ (# p,q #) -> (p,q)
504 Indeed, the bindings can even be recursive.
511 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
513 <sect1 id="syntax-extns">
514 <title>Syntactic extensions</title>
516 <!-- ====================== HIERARCHICAL MODULES ======================= -->
518 <sect2 id="hierarchical-modules">
519 <title>Hierarchical Modules</title>
521 <para>GHC supports a small extension to the syntax of module
522 names: a module name is allowed to contain a dot
523 <literal>‘.’</literal>. This is also known as the
524 “hierarchical module namespace” extension, because
525 it extends the normally flat Haskell module namespace into a
526 more flexible hierarchy of modules.</para>
528 <para>This extension has very little impact on the language
529 itself; modules names are <emphasis>always</emphasis> fully
530 qualified, so you can just think of the fully qualified module
531 name as <quote>the module name</quote>. In particular, this
532 means that the full module name must be given after the
533 <literal>module</literal> keyword at the beginning of the
534 module; for example, the module <literal>A.B.C</literal> must
537 <programlisting>module A.B.C</programlisting>
540 <para>It is a common strategy to use the <literal>as</literal>
541 keyword to save some typing when using qualified names with
542 hierarchical modules. For example:</para>
545 import qualified Control.Monad.ST.Strict as ST
548 <para>For details on how GHC searches for source and interface
549 files in the presence of hierarchical modules, see <xref
550 linkend="search-path"/>.</para>
552 <para>GHC comes with a large collection of libraries arranged
553 hierarchically; see the accompanying <ulink
554 url="../libraries/index.html">library
555 documentation</ulink>. More libraries to install are available
557 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
560 <!-- ====================== PATTERN GUARDS ======================= -->
562 <sect2 id="pattern-guards">
563 <title>Pattern guards</title>
566 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
567 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.)
571 Suppose we have an abstract data type of finite maps, with a
575 lookup :: FiniteMap -> Int -> Maybe Int
578 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
579 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
583 clunky env var1 var2 | ok1 && ok2 = val1 + val2
584 | otherwise = var1 + var2
595 The auxiliary functions are
599 maybeToBool :: Maybe a -> Bool
600 maybeToBool (Just x) = True
601 maybeToBool Nothing = False
603 expectJust :: Maybe a -> a
604 expectJust (Just x) = x
605 expectJust Nothing = error "Unexpected Nothing"
609 What is <function>clunky</function> doing? The guard <literal>ok1 &&
610 ok2</literal> checks that both lookups succeed, using
611 <function>maybeToBool</function> to convert the <function>Maybe</function>
612 types to booleans. The (lazily evaluated) <function>expectJust</function>
613 calls extract the values from the results of the lookups, and binds the
614 returned values to <varname>val1</varname> and <varname>val2</varname>
615 respectively. If either lookup fails, then clunky takes the
616 <literal>otherwise</literal> case and returns the sum of its arguments.
620 This is certainly legal Haskell, but it is a tremendously verbose and
621 un-obvious way to achieve the desired effect. Arguably, a more direct way
622 to write clunky would be to use case expressions:
626 clunky env var1 var2 = case lookup env var1 of
628 Just val1 -> case lookup env var2 of
630 Just val2 -> val1 + val2
636 This is a bit shorter, but hardly better. Of course, we can rewrite any set
637 of pattern-matching, guarded equations as case expressions; that is
638 precisely what the compiler does when compiling equations! The reason that
639 Haskell provides guarded equations is because they allow us to write down
640 the cases we want to consider, one at a time, independently of each other.
641 This structure is hidden in the case version. Two of the right-hand sides
642 are really the same (<function>fail</function>), and the whole expression
643 tends to become more and more indented.
647 Here is how I would write clunky:
652 | Just val1 <- lookup env var1
653 , Just val2 <- lookup env var2
655 ...other equations for clunky...
659 The semantics should be clear enough. The qualifiers are matched in order.
660 For a <literal><-</literal> qualifier, which I call a pattern guard, the
661 right hand side is evaluated and matched against the pattern on the left.
662 If the match fails then the whole guard fails and the next equation is
663 tried. If it succeeds, then the appropriate binding takes place, and the
664 next qualifier is matched, in the augmented environment. Unlike list
665 comprehensions, however, the type of the expression to the right of the
666 <literal><-</literal> is the same as the type of the pattern to its
667 left. The bindings introduced by pattern guards scope over all the
668 remaining guard qualifiers, and over the right hand side of the equation.
672 Just as with list comprehensions, boolean expressions can be freely mixed
673 with among the pattern guards. For example:
684 Haskell's current guards therefore emerge as a special case, in which the
685 qualifier list has just one element, a boolean expression.
689 <!-- ===================== Recursive do-notation =================== -->
691 <sect2 id="mdo-notation">
692 <title>The recursive do-notation
695 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
696 "A recursive do for Haskell",
697 Levent Erkok, John Launchbury",
698 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
701 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
702 that is, the variables bound in a do-expression are visible only in the textually following
703 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
704 group. It turns out that several applications can benefit from recursive bindings in
705 the do-notation, and this extension provides the necessary syntactic support.
708 Here is a simple (yet contrived) example:
711 import Control.Monad.Fix
713 justOnes = mdo xs <- Just (1:xs)
717 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
721 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
724 class Monad m => MonadFix m where
725 mfix :: (a -> m a) -> m a
728 The function <literal>mfix</literal>
729 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
730 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
731 For details, see the above mentioned reference.
734 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
735 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
736 for Haskell's internal state monad (strict and lazy, respectively).
739 There are three important points in using the recursive-do notation:
742 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
743 than <literal>do</literal>).
747 You should <literal>import Control.Monad.Fix</literal>.
748 (Note: Strictly speaking, this import is required only when you need to refer to the name
749 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
750 are encouraged to always import this module when using the mdo-notation.)
754 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
760 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
761 contains up to date information on recursive monadic bindings.
765 Historical note: The old implementation of the mdo-notation (and most
766 of the existing documents) used the name
767 <literal>MonadRec</literal> for the class and the corresponding library.
768 This name is not supported by GHC.
774 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
776 <sect2 id="parallel-list-comprehensions">
777 <title>Parallel List Comprehensions</title>
778 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
780 <indexterm><primary>parallel list comprehensions</primary>
783 <para>Parallel list comprehensions are a natural extension to list
784 comprehensions. List comprehensions can be thought of as a nice
785 syntax for writing maps and filters. Parallel comprehensions
786 extend this to include the zipWith family.</para>
788 <para>A parallel list comprehension has multiple independent
789 branches of qualifier lists, each separated by a `|' symbol. For
790 example, the following zips together two lists:</para>
793 [ (x, y) | x <- xs | y <- ys ]
796 <para>The behavior of parallel list comprehensions follows that of
797 zip, in that the resulting list will have the same length as the
798 shortest branch.</para>
800 <para>We can define parallel list comprehensions by translation to
801 regular comprehensions. Here's the basic idea:</para>
803 <para>Given a parallel comprehension of the form: </para>
806 [ e | p1 <- e11, p2 <- e12, ...
807 | q1 <- e21, q2 <- e22, ...
812 <para>This will be translated to: </para>
815 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
816 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
821 <para>where `zipN' is the appropriate zip for the given number of
826 <sect2 id="rebindable-syntax">
827 <title>Rebindable syntax</title>
830 <para>GHC allows most kinds of built-in syntax to be rebound by
831 the user, to facilitate replacing the <literal>Prelude</literal>
832 with a home-grown version, for example.</para>
834 <para>You may want to define your own numeric class
835 hierarchy. It completely defeats that purpose if the
836 literal "1" means "<literal>Prelude.fromInteger
837 1</literal>", which is what the Haskell Report specifies.
838 So the <option>-fno-implicit-prelude</option> flag causes
839 the following pieces of built-in syntax to refer to
840 <emphasis>whatever is in scope</emphasis>, not the Prelude
845 <para>An integer literal <literal>368</literal> means
846 "<literal>fromInteger (368::Integer)</literal>", rather than
847 "<literal>Prelude.fromInteger (368::Integer)</literal>".
850 <listitem><para>Fractional literals are handed in just the same way,
851 except that the translation is
852 <literal>fromRational (3.68::Rational)</literal>.
855 <listitem><para>The equality test in an overloaded numeric pattern
856 uses whatever <literal>(==)</literal> is in scope.
859 <listitem><para>The subtraction operation, and the
860 greater-than-or-equal test, in <literal>n+k</literal> patterns
861 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
865 <para>Negation (e.g. "<literal>- (f x)</literal>")
866 means "<literal>negate (f x)</literal>", both in numeric
867 patterns, and expressions.
871 <para>"Do" notation is translated using whatever
872 functions <literal>(>>=)</literal>,
873 <literal>(>>)</literal>, and <literal>fail</literal>,
874 are in scope (not the Prelude
875 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
876 comprehensions, are unaffected. </para></listitem>
880 notation (see <xref linkend="arrow-notation"/>)
881 uses whatever <literal>arr</literal>,
882 <literal>(>>>)</literal>, <literal>first</literal>,
883 <literal>app</literal>, <literal>(|||)</literal> and
884 <literal>loop</literal> functions are in scope. But unlike the
885 other constructs, the types of these functions must match the
886 Prelude types very closely. Details are in flux; if you want
890 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
891 even if that is a little unexpected. For emample, the
892 static semantics of the literal <literal>368</literal>
893 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
894 <literal>fromInteger</literal> to have any of the types:
896 fromInteger :: Integer -> Integer
897 fromInteger :: forall a. Foo a => Integer -> a
898 fromInteger :: Num a => a -> Integer
899 fromInteger :: Integer -> Bool -> Bool
903 <para>Be warned: this is an experimental facility, with
904 fewer checks than usual. Use <literal>-dcore-lint</literal>
905 to typecheck the desugared program. If Core Lint is happy
906 you should be all right.</para>
910 <sect2 id="postfix-operators">
911 <title>Postfix operators</title>
914 GHC allows a small extension to the syntax of left operator sections, which
915 allows you to define postfix operators. The extension is this: the left section
919 is equivalent (from the point of view of both type checking and execution) to the expression
923 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
924 The strict Haskell 98 interpretation is that the section is equivalent to
928 That is, the operator must be a function of two arguments. GHC allows it to
929 take only one argument, and that in turn allows you to write the function
932 <para>Since this extension goes beyond Haskell 98, it should really be enabled
933 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
934 change their behaviour, of course.)
936 <para>The extension does not extend to the left-hand side of function
937 definitions; you must define such a function in prefix form.</para>
944 <!-- TYPE SYSTEM EXTENSIONS -->
945 <sect1 id="data-type-extensions">
946 <title>Extensions to data types and type synonyms</title>
948 <sect2 id="nullary-types">
949 <title>Data types with no constructors</title>
951 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
952 a data type with no constructors. For example:</para>
956 data T a -- T :: * -> *
959 <para>Syntactically, the declaration lacks the "= constrs" part. The
960 type can be parameterised over types of any kind, but if the kind is
961 not <literal>*</literal> then an explicit kind annotation must be used
962 (see <xref linkend="kinding"/>).</para>
964 <para>Such data types have only one value, namely bottom.
965 Nevertheless, they can be useful when defining "phantom types".</para>
968 <sect2 id="infix-tycons">
969 <title>Infix type constructors, classes, and type variables</title>
972 GHC allows type constructors, classes, and type variables to be operators, and
973 to be written infix, very much like expressions. More specifically:
976 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
977 The lexical syntax is the same as that for data constructors.
980 Data type and type-synonym declarations can be written infix, parenthesised
981 if you want further arguments. E.g.
983 data a :*: b = Foo a b
984 type a :+: b = Either a b
985 class a :=: b where ...
987 data (a :**: b) x = Baz a b x
988 type (a :++: b) y = Either (a,b) y
992 Types, and class constraints, can be written infix. For example
995 f :: (a :=: b) => a -> b
999 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1000 The lexical syntax is the same as that for variable operators, excluding "(.)",
1001 "(!)", and "(*)". In a binding position, the operator must be
1002 parenthesised. For example:
1004 type T (+) = Int + Int
1008 liftA2 :: Arrow (~>)
1009 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1015 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1016 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1019 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1020 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1021 sets the fixity for a data constructor and the corresponding type constructor. For example:
1025 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1026 and similarly for <literal>:*:</literal>.
1027 <literal>Int `a` Bool</literal>.
1030 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1037 <sect2 id="type-synonyms">
1038 <title>Liberalised type synonyms</title>
1041 Type synonyms are like macros at the type level, and
1042 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1043 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1045 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1046 in a type synonym, thus:
1048 type Discard a = forall b. Show b => a -> b -> (a, String)
1053 g :: Discard Int -> (Int,String) -- A rank-2 type
1060 You can write an unboxed tuple in a type synonym:
1062 type Pr = (# Int, Int #)
1070 You can apply a type synonym to a forall type:
1072 type Foo a = a -> a -> Bool
1074 f :: Foo (forall b. b->b)
1076 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1078 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1083 You can apply a type synonym to a partially applied type synonym:
1085 type Generic i o = forall x. i x -> o x
1088 foo :: Generic Id []
1090 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1092 foo :: forall x. x -> [x]
1100 GHC currently does kind checking before expanding synonyms (though even that
1104 After expanding type synonyms, GHC does validity checking on types, looking for
1105 the following mal-formedness which isn't detected simply by kind checking:
1108 Type constructor applied to a type involving for-alls.
1111 Unboxed tuple on left of an arrow.
1114 Partially-applied type synonym.
1118 this will be rejected:
1120 type Pr = (# Int, Int #)
1125 because GHC does not allow unboxed tuples on the left of a function arrow.
1130 <sect2 id="existential-quantification">
1131 <title>Existentially quantified data constructors
1135 The idea of using existential quantification in data type declarations
1136 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1137 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1138 London, 1991). It was later formalised by Laufer and Odersky
1139 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1140 TOPLAS, 16(5), pp1411-1430, 1994).
1141 It's been in Lennart
1142 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1143 proved very useful. Here's the idea. Consider the declaration:
1149 data Foo = forall a. MkFoo a (a -> Bool)
1156 The data type <literal>Foo</literal> has two constructors with types:
1162 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1169 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1170 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1171 For example, the following expression is fine:
1177 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1183 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1184 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1185 isUpper</function> packages a character with a compatible function. These
1186 two things are each of type <literal>Foo</literal> and can be put in a list.
1190 What can we do with a value of type <literal>Foo</literal>?. In particular,
1191 what happens when we pattern-match on <function>MkFoo</function>?
1197 f (MkFoo val fn) = ???
1203 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1204 are compatible, the only (useful) thing we can do with them is to
1205 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1212 f (MkFoo val fn) = fn val
1218 What this allows us to do is to package heterogenous values
1219 together with a bunch of functions that manipulate them, and then treat
1220 that collection of packages in a uniform manner. You can express
1221 quite a bit of object-oriented-like programming this way.
1224 <sect3 id="existential">
1225 <title>Why existential?
1229 What has this to do with <emphasis>existential</emphasis> quantification?
1230 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1236 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1242 But Haskell programmers can safely think of the ordinary
1243 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1244 adding a new existential quantification construct.
1250 <title>Type classes</title>
1253 An easy extension is to allow
1254 arbitrary contexts before the constructor. For example:
1260 data Baz = forall a. Eq a => Baz1 a a
1261 | forall b. Show b => Baz2 b (b -> b)
1267 The two constructors have the types you'd expect:
1273 Baz1 :: forall a. Eq a => a -> a -> Baz
1274 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1280 But when pattern matching on <function>Baz1</function> the matched values can be compared
1281 for equality, and when pattern matching on <function>Baz2</function> the first matched
1282 value can be converted to a string (as well as applying the function to it).
1283 So this program is legal:
1290 f (Baz1 p q) | p == q = "Yes"
1292 f (Baz2 v fn) = show (fn v)
1298 Operationally, in a dictionary-passing implementation, the
1299 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1300 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1301 extract it on pattern matching.
1305 Notice the way that the syntax fits smoothly with that used for
1306 universal quantification earlier.
1311 <sect3 id="existential-records">
1312 <title>Record Constructors</title>
1315 GHC allows existentials to be used with records syntax as well. For example:
1318 data Counter a = forall self. NewCounter
1320 , _inc :: self -> self
1321 , _display :: self -> IO ()
1325 Here <literal>tag</literal> is a public field, with a well-typed selector
1326 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1327 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1328 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1329 compile-time error. In other words, <emphasis>GHC defines a record selector function
1330 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1331 (This example used an underscore in the fields for which record selectors
1332 will not be defined, but that is only programming style; GHC ignores them.)
1336 To make use of these hidden fields, we need to create some helper functions:
1339 inc :: Counter a -> Counter a
1340 inc (NewCounter x i d t) = NewCounter
1341 { _this = i x, _inc = i, _display = d, tag = t }
1343 display :: Counter a -> IO ()
1344 display NewCounter{ _this = x, _display = d } = d x
1347 Now we can define counters with different underlying implementations:
1350 counterA :: Counter String
1351 counterA = NewCounter
1352 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1354 counterB :: Counter String
1355 counterB = NewCounter
1356 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1359 display (inc counterA) -- prints "1"
1360 display (inc (inc counterB)) -- prints "##"
1363 At the moment, record update syntax is only supported for Haskell 98 data types,
1364 so the following function does <emphasis>not</emphasis> work:
1367 -- This is invalid; use explicit NewCounter instead for now
1368 setTag :: Counter a -> a -> Counter a
1369 setTag obj t = obj{ tag = t }
1378 <title>Restrictions</title>
1381 There are several restrictions on the ways in which existentially-quantified
1382 constructors can be use.
1391 When pattern matching, each pattern match introduces a new,
1392 distinct, type for each existential type variable. These types cannot
1393 be unified with any other type, nor can they escape from the scope of
1394 the pattern match. For example, these fragments are incorrect:
1402 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1403 is the result of <function>f1</function>. One way to see why this is wrong is to
1404 ask what type <function>f1</function> has:
1408 f1 :: Foo -> a -- Weird!
1412 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1417 f1 :: forall a. Foo -> a -- Wrong!
1421 The original program is just plain wrong. Here's another sort of error
1425 f2 (Baz1 a b) (Baz1 p q) = a==q
1429 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1430 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1431 from the two <function>Baz1</function> constructors.
1439 You can't pattern-match on an existentially quantified
1440 constructor in a <literal>let</literal> or <literal>where</literal> group of
1441 bindings. So this is illegal:
1445 f3 x = a==b where { Baz1 a b = x }
1448 Instead, use a <literal>case</literal> expression:
1451 f3 x = case x of Baz1 a b -> a==b
1454 In general, you can only pattern-match
1455 on an existentially-quantified constructor in a <literal>case</literal> expression or
1456 in the patterns of a function definition.
1458 The reason for this restriction is really an implementation one.
1459 Type-checking binding groups is already a nightmare without
1460 existentials complicating the picture. Also an existential pattern
1461 binding at the top level of a module doesn't make sense, because it's
1462 not clear how to prevent the existentially-quantified type "escaping".
1463 So for now, there's a simple-to-state restriction. We'll see how
1471 You can't use existential quantification for <literal>newtype</literal>
1472 declarations. So this is illegal:
1476 newtype T = forall a. Ord a => MkT a
1480 Reason: a value of type <literal>T</literal> must be represented as a
1481 pair of a dictionary for <literal>Ord t</literal> and a value of type
1482 <literal>t</literal>. That contradicts the idea that
1483 <literal>newtype</literal> should have no concrete representation.
1484 You can get just the same efficiency and effect by using
1485 <literal>data</literal> instead of <literal>newtype</literal>. If
1486 there is no overloading involved, then there is more of a case for
1487 allowing an existentially-quantified <literal>newtype</literal>,
1488 because the <literal>data</literal> version does carry an
1489 implementation cost, but single-field existentially quantified
1490 constructors aren't much use. So the simple restriction (no
1491 existential stuff on <literal>newtype</literal>) stands, unless there
1492 are convincing reasons to change it.
1500 You can't use <literal>deriving</literal> to define instances of a
1501 data type with existentially quantified data constructors.
1503 Reason: in most cases it would not make sense. For example:;
1506 data T = forall a. MkT [a] deriving( Eq )
1509 To derive <literal>Eq</literal> in the standard way we would need to have equality
1510 between the single component of two <function>MkT</function> constructors:
1514 (MkT a) == (MkT b) = ???
1517 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1518 It's just about possible to imagine examples in which the derived instance
1519 would make sense, but it seems altogether simpler simply to prohibit such
1520 declarations. Define your own instances!
1531 <!-- ====================== Generalised algebraic data types ======================= -->
1533 <sect2 id="gadt-style">
1534 <title>Declaring data types with explicit constructor signatures</title>
1536 <para>GHC allows you to declare an algebraic data type by
1537 giving the type signatures of constructors explicitly. For example:
1541 Just :: a -> Maybe a
1543 The form is called a "GADT-style declaration"
1544 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1545 can only be declared using this form.</para>
1546 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1547 For example, these two declarations are equivalent:
1549 data Foo = forall a. MkFoo a (a -> Bool)
1550 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1553 <para>Any data type that can be declared in standard Haskell-98 syntax
1554 can also be declared using GADT-style syntax.
1555 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1556 they treat class constraints on the data constructors differently.
1557 Specifically, if the constructor is given a type-class context, that
1558 context is made available by pattern matching. For example:
1561 MkSet :: Eq a => [a] -> Set a
1563 makeSet :: Eq a => [a] -> Set a
1564 makeSet xs = MkSet (nub xs)
1566 insert :: a -> Set a -> Set a
1567 insert a (MkSet as) | a `elem` as = MkSet as
1568 | otherwise = MkSet (a:as)
1570 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1571 gives rise to a <literal>(Eq a)</literal>
1572 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1573 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1574 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1575 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1576 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1577 In the example, the equality dictionary is used to satisfy the equality constraint
1578 generated by the call to <literal>elem</literal>, so that the type of
1579 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1581 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1582 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1583 In Haskell 98 the defintion
1585 data Eq a => Set' a = MkSet' [a]
1587 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1588 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1589 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1590 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1591 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1593 For example, a possible application of GHC's behaviour is to reify dictionaries:
1595 data NumInst a where
1596 MkNumInst :: Num a => NumInst a
1598 intInst :: NumInst Int
1601 plus :: NumInst a -> a -> a -> a
1602 plus MkNumInst p q = p + q
1604 Here, a value of type <literal>NumInst a</literal> is equivalent
1605 to an explicit <literal>(Num a)</literal> dictionary.
1609 The rest of this section gives further details about GADT-style data
1614 The result type of each data constructor must begin with the type constructor being defined.
1615 If the result type of all constructors
1616 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1617 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1618 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1622 The type signature of
1623 each constructor is independent, and is implicitly universally quantified as usual.
1624 Different constructors may have different universally-quantified type variables
1625 and different type-class constraints.
1626 For example, this is fine:
1629 T1 :: Eq b => b -> T b
1630 T2 :: (Show c, Ix c) => c -> [c] -> T c
1635 Unlike a Haskell-98-style
1636 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1637 have no scope. Indeed, one can write a kind signature instead:
1639 data Set :: * -> * where ...
1641 or even a mixture of the two:
1643 data Foo a :: (* -> *) -> * where ...
1645 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1648 data Foo a (b :: * -> *) where ...
1654 You can use strictness annotations, in the obvious places
1655 in the constructor type:
1658 Lit :: !Int -> Term Int
1659 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1660 Pair :: Term a -> Term b -> Term (a,b)
1665 You can use a <literal>deriving</literal> clause on a GADT-style data type
1666 declaration. For example, these two declarations are equivalent
1668 data Maybe1 a where {
1669 Nothing1 :: Maybe1 a ;
1670 Just1 :: a -> Maybe1 a
1671 } deriving( Eq, Ord )
1673 data Maybe2 a = Nothing2 | Just2 a
1679 You can use record syntax on a GADT-style data type declaration:
1683 Adult { name :: String, children :: [Person] } :: Person
1684 Child { name :: String } :: Person
1686 As usual, for every constructor that has a field <literal>f</literal>, the type of
1687 field <literal>f</literal> must be the same (modulo alpha conversion).
1690 At the moment, record updates are not yet possible with GADT-style declarations,
1691 so support is limited to record construction, selection and pattern matching.
1694 aPerson = Adult { name = "Fred", children = [] }
1696 shortName :: Person -> Bool
1697 hasChildren (Adult { children = kids }) = not (null kids)
1698 hasChildren (Child {}) = False
1703 As in the case of existentials declared using the Haskell-98-like record syntax
1704 (<xref linkend="existential-records"/>),
1705 record-selector functions are generated only for those fields that have well-typed
1707 Here is the example of that section, in GADT-style syntax:
1709 data Counter a where
1710 NewCounter { _this :: self
1711 , _inc :: self -> self
1712 , _display :: self -> IO ()
1717 As before, only one selector function is generated here, that for <literal>tag</literal>.
1718 Nevertheless, you can still use all the field names in pattern matching and record construction.
1720 </itemizedlist></para>
1724 <title>Generalised Algebraic Data Types (GADTs)</title>
1726 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1727 by allowing constructors to have richer return types. Here is an example:
1730 Lit :: Int -> Term Int
1731 Succ :: Term Int -> Term Int
1732 IsZero :: Term Int -> Term Bool
1733 If :: Term Bool -> Term a -> Term a -> Term a
1734 Pair :: Term a -> Term b -> Term (a,b)
1736 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1737 case with ordinary data types. This generality allows us to
1738 write a well-typed <literal>eval</literal> function
1739 for these <literal>Terms</literal>:
1743 eval (Succ t) = 1 + eval t
1744 eval (IsZero t) = eval t == 0
1745 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1746 eval (Pair e1 e2) = (eval e1, eval e2)
1748 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1749 For example, in the right hand side of the equation
1754 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1755 A precise specification of the type rules is beyond what this user manual aspires to,
1756 but the design closely follows that described in
1758 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1759 unification-based type inference for GADTs</ulink>,
1761 The general principle is this: <emphasis>type refinement is only carried out
1762 based on user-supplied type annotations</emphasis>.
1763 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1764 and lots of obscure error messages will
1765 occur. However, the refinement is quite general. For example, if we had:
1767 eval :: Term a -> a -> a
1768 eval (Lit i) j = i+j
1770 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1771 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1772 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1775 These and many other examples are given in papers by Hongwei Xi, and
1776 Tim Sheard. There is a longer introduction
1777 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1779 <ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
1780 may use different notation to that implemented in GHC.
1783 The rest of this section outlines the extensions to GHC that support GADTs.
1786 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1787 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1788 The result type of each constructor must begin with the type constructor being defined,
1789 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1790 For example, in the <literal>Term</literal> data
1791 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1792 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1797 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1798 an ordianary data type.
1802 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1806 Lit { val :: Int } :: Term Int
1807 Succ { num :: Term Int } :: Term Int
1808 Pred { num :: Term Int } :: Term Int
1809 IsZero { arg :: Term Int } :: Term Bool
1810 Pair { arg1 :: Term a
1813 If { cnd :: Term Bool
1818 However, for GADTs there is the following additional constraint:
1819 every constructor that has a field <literal>f</literal> must have
1820 the same result type (modulo alpha conversion)
1821 Hence, in the above example, we cannot merge the <literal>num</literal>
1822 and <literal>arg</literal> fields above into a
1823 single name. Although their field types are both <literal>Term Int</literal>,
1824 their selector functions actually have different types:
1827 num :: Term Int -> Term Int
1828 arg :: Term Bool -> Term Int
1837 <!-- ====================== End of Generalised algebraic data types ======================= -->
1840 <sect2 id="deriving-typeable">
1841 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1844 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1845 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1846 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1847 classes <literal>Eq</literal>, <literal>Ord</literal>,
1848 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1851 GHC extends this list with two more classes that may be automatically derived
1852 (provided the <option>-fglasgow-exts</option> flag is specified):
1853 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1854 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1855 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1857 <para>An instance of <literal>Typeable</literal> can only be derived if the
1858 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1859 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1861 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1862 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1864 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1865 are used, and only <literal>Typeable1</literal> up to
1866 <literal>Typeable7</literal> are provided in the library.)
1867 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1868 class, whose kind suits that of the data type constructor, and
1869 then writing the data type instance by hand.
1873 <sect2 id="newtype-deriving">
1874 <title>Generalised derived instances for newtypes</title>
1877 When you define an abstract type using <literal>newtype</literal>, you may want
1878 the new type to inherit some instances from its representation. In
1879 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1880 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1881 other classes you have to write an explicit instance declaration. For
1882 example, if you define
1885 newtype Dollars = Dollars Int
1888 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1889 explicitly define an instance of <literal>Num</literal>:
1892 instance Num Dollars where
1893 Dollars a + Dollars b = Dollars (a+b)
1896 All the instance does is apply and remove the <literal>newtype</literal>
1897 constructor. It is particularly galling that, since the constructor
1898 doesn't appear at run-time, this instance declaration defines a
1899 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1900 dictionary, only slower!
1904 <sect3> <title> Generalising the deriving clause </title>
1906 GHC now permits such instances to be derived instead, so one can write
1908 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1911 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1912 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1913 derives an instance declaration of the form
1916 instance Num Int => Num Dollars
1919 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1923 We can also derive instances of constructor classes in a similar
1924 way. For example, suppose we have implemented state and failure monad
1925 transformers, such that
1928 instance Monad m => Monad (State s m)
1929 instance Monad m => Monad (Failure m)
1931 In Haskell 98, we can define a parsing monad by
1933 type Parser tok m a = State [tok] (Failure m) a
1936 which is automatically a monad thanks to the instance declarations
1937 above. With the extension, we can make the parser type abstract,
1938 without needing to write an instance of class <literal>Monad</literal>, via
1941 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1944 In this case the derived instance declaration is of the form
1946 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
1949 Notice that, since <literal>Monad</literal> is a constructor class, the
1950 instance is a <emphasis>partial application</emphasis> of the new type, not the
1951 entire left hand side. We can imagine that the type declaration is
1952 ``eta-converted'' to generate the context of the instance
1957 We can even derive instances of multi-parameter classes, provided the
1958 newtype is the last class parameter. In this case, a ``partial
1959 application'' of the class appears in the <literal>deriving</literal>
1960 clause. For example, given the class
1963 class StateMonad s m | m -> s where ...
1964 instance Monad m => StateMonad s (State s m) where ...
1966 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
1968 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1969 deriving (Monad, StateMonad [tok])
1972 The derived instance is obtained by completing the application of the
1973 class to the new type:
1976 instance StateMonad [tok] (State [tok] (Failure m)) =>
1977 StateMonad [tok] (Parser tok m)
1982 As a result of this extension, all derived instances in newtype
1983 declarations are treated uniformly (and implemented just by reusing
1984 the dictionary for the representation type), <emphasis>except</emphasis>
1985 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
1986 the newtype and its representation.
1990 <sect3> <title> A more precise specification </title>
1992 Derived instance declarations are constructed as follows. Consider the
1993 declaration (after expansion of any type synonyms)
1996 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2002 The <literal>ci</literal> are partial applications of
2003 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2004 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2007 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2010 The type <literal>t</literal> is an arbitrary type.
2013 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2014 nor in the <literal>ci</literal>, and
2017 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2018 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2019 should not "look through" the type or its constructor. You can still
2020 derive these classes for a newtype, but it happens in the usual way, not
2021 via this new mechanism.
2024 Then, for each <literal>ci</literal>, the derived instance
2027 instance ci t => ci (T v1...vk)
2029 As an example which does <emphasis>not</emphasis> work, consider
2031 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2033 Here we cannot derive the instance
2035 instance Monad (State s m) => Monad (NonMonad m)
2038 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2039 and so cannot be "eta-converted" away. It is a good thing that this
2040 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2041 not, in fact, a monad --- for the same reason. Try defining
2042 <literal>>>=</literal> with the correct type: you won't be able to.
2046 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2047 important, since we can only derive instances for the last one. If the
2048 <literal>StateMonad</literal> class above were instead defined as
2051 class StateMonad m s | m -> s where ...
2054 then we would not have been able to derive an instance for the
2055 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2056 classes usually have one "main" parameter for which deriving new
2057 instances is most interesting.
2059 <para>Lastly, all of this applies only for classes other than
2060 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2061 and <literal>Data</literal>, for which the built-in derivation applies (section
2062 4.3.3. of the Haskell Report).
2063 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2064 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2065 the standard method is used or the one described here.)
2071 <sect2 id="stand-alone-deriving">
2072 <title>Stand-alone deriving declarations</title>
2075 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2077 data Foo a = Bar a | Baz String
2079 derive instance Eq (Foo a)
2081 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2082 you can use it as a variable name elsewhere.</para>
2083 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2084 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2087 newtype Foo a = MkFoo (State Int a)
2089 derive instance MonadState Int Foo
2091 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2092 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2100 <!-- TYPE SYSTEM EXTENSIONS -->
2101 <sect1 id="other-type-extensions">
2102 <title>Other type system extensions</title>
2104 <sect2 id="multi-param-type-classes">
2105 <title>Class declarations</title>
2108 This section, and the next one, documents GHC's type-class extensions.
2109 There's lots of background in the paper <ulink
2110 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2111 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2112 Jones, Erik Meijer).
2115 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2119 <title>Multi-parameter type classes</title>
2121 Multi-parameter type classes are permitted. For example:
2125 class Collection c a where
2126 union :: c a -> c a -> c a
2134 <title>The superclasses of a class declaration</title>
2137 There are no restrictions on the context in a class declaration
2138 (which introduces superclasses), except that the class hierarchy must
2139 be acyclic. So these class declarations are OK:
2143 class Functor (m k) => FiniteMap m k where
2146 class (Monad m, Monad (t m)) => Transform t m where
2147 lift :: m a -> (t m) a
2153 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2154 of "acyclic" involves only the superclass relationships. For example,
2160 op :: D b => a -> b -> b
2163 class C a => D a where { ... }
2167 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2168 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2169 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2176 <sect3 id="class-method-types">
2177 <title>Class method types</title>
2180 Haskell 98 prohibits class method types to mention constraints on the
2181 class type variable, thus:
2184 fromList :: [a] -> s a
2185 elem :: Eq a => a -> s a -> Bool
2187 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2188 contains the constraint <literal>Eq a</literal>, constrains only the
2189 class type variable (in this case <literal>a</literal>).
2190 GHC lifts this restriction.
2197 <sect2 id="functional-dependencies">
2198 <title>Functional dependencies
2201 <para> Functional dependencies are implemented as described by Mark Jones
2202 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2203 In Proceedings of the 9th European Symposium on Programming,
2204 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2208 Functional dependencies are introduced by a vertical bar in the syntax of a
2209 class declaration; e.g.
2211 class (Monad m) => MonadState s m | m -> s where ...
2213 class Foo a b c | a b -> c where ...
2215 There should be more documentation, but there isn't (yet). Yell if you need it.
2218 <sect3><title>Rules for functional dependencies </title>
2220 In a class declaration, all of the class type variables must be reachable (in the sense
2221 mentioned in <xref linkend="type-restrictions"/>)
2222 from the free variables of each method type.
2226 class Coll s a where
2228 insert :: s -> a -> s
2231 is not OK, because the type of <literal>empty</literal> doesn't mention
2232 <literal>a</literal>. Functional dependencies can make the type variable
2235 class Coll s a | s -> a where
2237 insert :: s -> a -> s
2240 Alternatively <literal>Coll</literal> might be rewritten
2243 class Coll s a where
2245 insert :: s a -> a -> s a
2249 which makes the connection between the type of a collection of
2250 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2251 Occasionally this really doesn't work, in which case you can split the
2259 class CollE s => Coll s a where
2260 insert :: s -> a -> s
2267 <title>Background on functional dependencies</title>
2269 <para>The following description of the motivation and use of functional dependencies is taken
2270 from the Hugs user manual, reproduced here (with minor changes) by kind
2271 permission of Mark Jones.
2274 Consider the following class, intended as part of a
2275 library for collection types:
2277 class Collects e ce where
2279 insert :: e -> ce -> ce
2280 member :: e -> ce -> Bool
2282 The type variable e used here represents the element type, while ce is the type
2283 of the container itself. Within this framework, we might want to define
2284 instances of this class for lists or characteristic functions (both of which
2285 can be used to represent collections of any equality type), bit sets (which can
2286 be used to represent collections of characters), or hash tables (which can be
2287 used to represent any collection whose elements have a hash function). Omitting
2288 standard implementation details, this would lead to the following declarations:
2290 instance Eq e => Collects e [e] where ...
2291 instance Eq e => Collects e (e -> Bool) where ...
2292 instance Collects Char BitSet where ...
2293 instance (Hashable e, Collects a ce)
2294 => Collects e (Array Int ce) where ...
2296 All this looks quite promising; we have a class and a range of interesting
2297 implementations. Unfortunately, there are some serious problems with the class
2298 declaration. First, the empty function has an ambiguous type:
2300 empty :: Collects e ce => ce
2302 By "ambiguous" we mean that there is a type variable e that appears on the left
2303 of the <literal>=></literal> symbol, but not on the right. The problem with
2304 this is that, according to the theoretical foundations of Haskell overloading,
2305 we cannot guarantee a well-defined semantics for any term with an ambiguous
2309 We can sidestep this specific problem by removing the empty member from the
2310 class declaration. However, although the remaining members, insert and member,
2311 do not have ambiguous types, we still run into problems when we try to use
2312 them. For example, consider the following two functions:
2314 f x y = insert x . insert y
2317 for which GHC infers the following types:
2319 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2320 g :: (Collects Bool c, Collects Char c) => c -> c
2322 Notice that the type for f allows the two parameters x and y to be assigned
2323 different types, even though it attempts to insert each of the two values, one
2324 after the other, into the same collection. If we're trying to model collections
2325 that contain only one type of value, then this is clearly an inaccurate
2326 type. Worse still, the definition for g is accepted, without causing a type
2327 error. As a result, the error in this code will not be flagged at the point
2328 where it appears. Instead, it will show up only when we try to use g, which
2329 might even be in a different module.
2332 <sect4><title>An attempt to use constructor classes</title>
2335 Faced with the problems described above, some Haskell programmers might be
2336 tempted to use something like the following version of the class declaration:
2338 class Collects e c where
2340 insert :: e -> c e -> c e
2341 member :: e -> c e -> Bool
2343 The key difference here is that we abstract over the type constructor c that is
2344 used to form the collection type c e, and not over that collection type itself,
2345 represented by ce in the original class declaration. This avoids the immediate
2346 problems that we mentioned above: empty has type <literal>Collects e c => c
2347 e</literal>, which is not ambiguous.
2350 The function f from the previous section has a more accurate type:
2352 f :: (Collects e c) => e -> e -> c e -> c e
2354 The function g from the previous section is now rejected with a type error as
2355 we would hope because the type of f does not allow the two arguments to have
2357 This, then, is an example of a multiple parameter class that does actually work
2358 quite well in practice, without ambiguity problems.
2359 There is, however, a catch. This version of the Collects class is nowhere near
2360 as general as the original class seemed to be: only one of the four instances
2361 for <literal>Collects</literal>
2362 given above can be used with this version of Collects because only one of
2363 them---the instance for lists---has a collection type that can be written in
2364 the form c e, for some type constructor c, and element type e.
2368 <sect4><title>Adding functional dependencies</title>
2371 To get a more useful version of the Collects class, Hugs provides a mechanism
2372 that allows programmers to specify dependencies between the parameters of a
2373 multiple parameter class (For readers with an interest in theoretical
2374 foundations and previous work: The use of dependency information can be seen
2375 both as a generalization of the proposal for `parametric type classes' that was
2376 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2377 later framework for "improvement" of qualified types. The
2378 underlying ideas are also discussed in a more theoretical and abstract setting
2379 in a manuscript [implparam], where they are identified as one point in a
2380 general design space for systems of implicit parameterization.).
2382 To start with an abstract example, consider a declaration such as:
2384 class C a b where ...
2386 which tells us simply that C can be thought of as a binary relation on types
2387 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2388 included in the definition of classes to add information about dependencies
2389 between parameters, as in the following examples:
2391 class D a b | a -> b where ...
2392 class E a b | a -> b, b -> a where ...
2394 The notation <literal>a -> b</literal> used here between the | and where
2395 symbols --- not to be
2396 confused with a function type --- indicates that the a parameter uniquely
2397 determines the b parameter, and might be read as "a determines b." Thus D is
2398 not just a relation, but actually a (partial) function. Similarly, from the two
2399 dependencies that are included in the definition of E, we can see that E
2400 represents a (partial) one-one mapping between types.
2403 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2404 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2405 m>=0, meaning that the y parameters are uniquely determined by the x
2406 parameters. Spaces can be used as separators if more than one variable appears
2407 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2408 annotated with multiple dependencies using commas as separators, as in the
2409 definition of E above. Some dependencies that we can write in this notation are
2410 redundant, and will be rejected because they don't serve any useful
2411 purpose, and may instead indicate an error in the program. Examples of
2412 dependencies like this include <literal>a -> a </literal>,
2413 <literal>a -> a a </literal>,
2414 <literal>a -> </literal>, etc. There can also be
2415 some redundancy if multiple dependencies are given, as in
2416 <literal>a->b</literal>,
2417 <literal>b->c </literal>, <literal>a->c </literal>, and
2418 in which some subset implies the remaining dependencies. Examples like this are
2419 not treated as errors. Note that dependencies appear only in class
2420 declarations, and not in any other part of the language. In particular, the
2421 syntax for instance declarations, class constraints, and types is completely
2425 By including dependencies in a class declaration, we provide a mechanism for
2426 the programmer to specify each multiple parameter class more precisely. The
2427 compiler, on the other hand, is responsible for ensuring that the set of
2428 instances that are in scope at any given point in the program is consistent
2429 with any declared dependencies. For example, the following pair of instance
2430 declarations cannot appear together in the same scope because they violate the
2431 dependency for D, even though either one on its own would be acceptable:
2433 instance D Bool Int where ...
2434 instance D Bool Char where ...
2436 Note also that the following declaration is not allowed, even by itself:
2438 instance D [a] b where ...
2440 The problem here is that this instance would allow one particular choice of [a]
2441 to be associated with more than one choice for b, which contradicts the
2442 dependency specified in the definition of D. More generally, this means that,
2443 in any instance of the form:
2445 instance D t s where ...
2447 for some particular types t and s, the only variables that can appear in s are
2448 the ones that appear in t, and hence, if the type t is known, then s will be
2449 uniquely determined.
2452 The benefit of including dependency information is that it allows us to define
2453 more general multiple parameter classes, without ambiguity problems, and with
2454 the benefit of more accurate types. To illustrate this, we return to the
2455 collection class example, and annotate the original definition of <literal>Collects</literal>
2456 with a simple dependency:
2458 class Collects e ce | ce -> e where
2460 insert :: e -> ce -> ce
2461 member :: e -> ce -> Bool
2463 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2464 determined by the type of the collection ce. Note that both parameters of
2465 Collects are of kind *; there are no constructor classes here. Note too that
2466 all of the instances of Collects that we gave earlier can be used
2467 together with this new definition.
2470 What about the ambiguity problems that we encountered with the original
2471 definition? The empty function still has type Collects e ce => ce, but it is no
2472 longer necessary to regard that as an ambiguous type: Although the variable e
2473 does not appear on the right of the => symbol, the dependency for class
2474 Collects tells us that it is uniquely determined by ce, which does appear on
2475 the right of the => symbol. Hence the context in which empty is used can still
2476 give enough information to determine types for both ce and e, without
2477 ambiguity. More generally, we need only regard a type as ambiguous if it
2478 contains a variable on the left of the => that is not uniquely determined
2479 (either directly or indirectly) by the variables on the right.
2482 Dependencies also help to produce more accurate types for user defined
2483 functions, and hence to provide earlier detection of errors, and less cluttered
2484 types for programmers to work with. Recall the previous definition for a
2487 f x y = insert x y = insert x . insert y
2489 for which we originally obtained a type:
2491 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2493 Given the dependency information that we have for Collects, however, we can
2494 deduce that a and b must be equal because they both appear as the second
2495 parameter in a Collects constraint with the same first parameter c. Hence we
2496 can infer a shorter and more accurate type for f:
2498 f :: (Collects a c) => a -> a -> c -> c
2500 In a similar way, the earlier definition of g will now be flagged as a type error.
2503 Although we have given only a few examples here, it should be clear that the
2504 addition of dependency information can help to make multiple parameter classes
2505 more useful in practice, avoiding ambiguity problems, and allowing more general
2506 sets of instance declarations.
2512 <sect2 id="instance-decls">
2513 <title>Instance declarations</title>
2515 <sect3 id="instance-rules">
2516 <title>Relaxed rules for instance declarations</title>
2518 <para>An instance declaration has the form
2520 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 ...
2522 The part before the "<literal>=></literal>" is the
2523 <emphasis>context</emphasis>, while the part after the
2524 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2528 In Haskell 98 the head of an instance declaration
2529 must be of the form <literal>C (T a1 ... an)</literal>, where
2530 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2531 and the <literal>a1 ... an</literal> are distinct type variables.
2532 Furthermore, the assertions in the context of the instance declaration
2533 must be of the form <literal>C a</literal> where <literal>a</literal>
2534 is a type variable that occurs in the head.
2537 The <option>-fglasgow-exts</option> flag loosens these restrictions
2538 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2539 the context and head of the instance declaration can each consist of arbitrary
2540 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2544 The Paterson Conditions: for each assertion in the context
2546 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2547 <listitem><para>The assertion has fewer constructors and variables (taken together
2548 and counting repetitions) than the head</para></listitem>
2552 <listitem><para>The Coverage Condition. For each functional dependency,
2553 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2554 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2555 every type variable in
2556 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2557 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2558 substitution mapping each type variable in the class declaration to the
2559 corresponding type in the instance declaration.
2562 These restrictions ensure that context reduction terminates: each reduction
2563 step makes the problem smaller by at least one
2564 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2565 if you give the <option>-fallow-undecidable-instances</option>
2566 flag (<xref linkend="undecidable-instances"/>).
2567 You can find lots of background material about the reason for these
2568 restrictions in the paper <ulink
2569 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2570 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2573 For example, these are OK:
2575 instance C Int [a] -- Multiple parameters
2576 instance Eq (S [a]) -- Structured type in head
2578 -- Repeated type variable in head
2579 instance C4 a a => C4 [a] [a]
2580 instance Stateful (ST s) (MutVar s)
2582 -- Head can consist of type variables only
2584 instance (Eq a, Show b) => C2 a b
2586 -- Non-type variables in context
2587 instance Show (s a) => Show (Sized s a)
2588 instance C2 Int a => C3 Bool [a]
2589 instance C2 Int a => C3 [a] b
2593 -- Context assertion no smaller than head
2594 instance C a => C a where ...
2595 -- (C b b) has more more occurrences of b than the head
2596 instance C b b => Foo [b] where ...
2601 The same restrictions apply to instances generated by
2602 <literal>deriving</literal> clauses. Thus the following is accepted:
2604 data MinHeap h a = H a (h a)
2607 because the derived instance
2609 instance (Show a, Show (h a)) => Show (MinHeap h a)
2611 conforms to the above rules.
2615 A useful idiom permitted by the above rules is as follows.
2616 If one allows overlapping instance declarations then it's quite
2617 convenient to have a "default instance" declaration that applies if
2618 something more specific does not:
2626 <sect3 id="undecidable-instances">
2627 <title>Undecidable instances</title>
2630 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2631 For example, sometimes you might want to use the following to get the
2632 effect of a "class synonym":
2634 class (C1 a, C2 a, C3 a) => C a where { }
2636 instance (C1 a, C2 a, C3 a) => C a where { }
2638 This allows you to write shorter signatures:
2644 f :: (C1 a, C2 a, C3 a) => ...
2646 The restrictions on functional dependencies (<xref
2647 linkend="functional-dependencies"/>) are particularly troublesome.
2648 It is tempting to introduce type variables in the context that do not appear in
2649 the head, something that is excluded by the normal rules. For example:
2651 class HasConverter a b | a -> b where
2654 data Foo a = MkFoo a
2656 instance (HasConverter a b,Show b) => Show (Foo a) where
2657 show (MkFoo value) = show (convert value)
2659 This is dangerous territory, however. Here, for example, is a program that would make the
2664 instance F [a] [[a]]
2665 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2667 Similarly, it can be tempting to lift the coverage condition:
2669 class Mul a b c | a b -> c where
2670 (.*.) :: a -> b -> c
2672 instance Mul Int Int Int where (.*.) = (*)
2673 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2674 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2676 The third instance declaration does not obey the coverage condition;
2677 and indeed the (somewhat strange) definition:
2679 f = \ b x y -> if b then x .*. [y] else y
2681 makes instance inference go into a loop, because it requires the constraint
2682 <literal>(Mul a [b] b)</literal>.
2685 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2686 the experimental flag <option>-fallow-undecidable-instances</option>
2687 <indexterm><primary>-fallow-undecidable-instances
2688 option</primary></indexterm>, both the Paterson Conditions and the Coverage Condition
2689 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2690 fixed-depth recursion stack. If you exceed the stack depth you get a
2691 sort of backtrace, and the opportunity to increase the stack depth
2692 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2698 <sect3 id="instance-overlap">
2699 <title>Overlapping instances</title>
2701 In general, <emphasis>GHC requires that that it be unambiguous which instance
2703 should be used to resolve a type-class constraint</emphasis>. This behaviour
2704 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2705 <indexterm><primary>-fallow-overlapping-instances
2706 </primary></indexterm>
2707 and <option>-fallow-incoherent-instances</option>
2708 <indexterm><primary>-fallow-incoherent-instances
2709 </primary></indexterm>, as this section discusses. Both these
2710 flags are dynamic flags, and can be set on a per-module basis, using
2711 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2713 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2714 it tries to match every instance declaration against the
2716 by instantiating the head of the instance declaration. For example, consider
2719 instance context1 => C Int a where ... -- (A)
2720 instance context2 => C a Bool where ... -- (B)
2721 instance context3 => C Int [a] where ... -- (C)
2722 instance context4 => C Int [Int] where ... -- (D)
2724 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2725 but (C) and (D) do not. When matching, GHC takes
2726 no account of the context of the instance declaration
2727 (<literal>context1</literal> etc).
2728 GHC's default behaviour is that <emphasis>exactly one instance must match the
2729 constraint it is trying to resolve</emphasis>.
2730 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2731 including both declarations (A) and (B), say); an error is only reported if a
2732 particular constraint matches more than one.
2736 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2737 more than one instance to match, provided there is a most specific one. For
2738 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2739 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2740 most-specific match, the program is rejected.
2743 However, GHC is conservative about committing to an overlapping instance. For example:
2748 Suppose that from the RHS of <literal>f</literal> we get the constraint
2749 <literal>C Int [b]</literal>. But
2750 GHC does not commit to instance (C), because in a particular
2751 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2752 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2753 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2754 GHC will instead pick (C), without complaining about
2755 the problem of subsequent instantiations.
2758 The willingness to be overlapped or incoherent is a property of
2759 the <emphasis>instance declaration</emphasis> itself, controlled by the
2760 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2761 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2762 being defined. Neither flag is required in a module that imports and uses the
2763 instance declaration. Specifically, during the lookup process:
2766 An instance declaration is ignored during the lookup process if (a) a more specific
2767 match is found, and (b) the instance declaration was compiled with
2768 <option>-fallow-overlapping-instances</option>. The flag setting for the
2769 more-specific instance does not matter.
2772 Suppose an instance declaration does not matche the constraint being looked up, but
2773 does unify with it, so that it might match when the constraint is further
2774 instantiated. Usually GHC will regard this as a reason for not committing to
2775 some other constraint. But if the instance declaration was compiled with
2776 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2777 check for that declaration.
2780 These rules make it possible for a library author to design a library that relies on
2781 overlapping instances without the library client having to know.
2784 If an instance declaration is compiled without
2785 <option>-fallow-overlapping-instances</option>,
2786 then that instance can never be overlapped. This could perhaps be
2787 inconvenient. Perhaps the rule should instead say that the
2788 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2789 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2790 at a usage site should be permitted regardless of how the instance declarations
2791 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2792 used at the usage site. (Mind you, the exact usage site can occasionally be
2793 hard to pin down.) We are interested to receive feedback on these points.
2795 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2796 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2801 <title>Type synonyms in the instance head</title>
2804 <emphasis>Unlike Haskell 98, instance heads may use type
2805 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2806 As always, using a type synonym is just shorthand for
2807 writing the RHS of the type synonym definition. For example:
2811 type Point = (Int,Int)
2812 instance C Point where ...
2813 instance C [Point] where ...
2817 is legal. However, if you added
2821 instance C (Int,Int) where ...
2825 as well, then the compiler will complain about the overlapping
2826 (actually, identical) instance declarations. As always, type synonyms
2827 must be fully applied. You cannot, for example, write:
2832 instance Monad P where ...
2836 This design decision is independent of all the others, and easily
2837 reversed, but it makes sense to me.
2845 <sect2 id="type-restrictions">
2846 <title>Type signatures</title>
2848 <sect3><title>The context of a type signature</title>
2850 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2851 the form <emphasis>(class type-variable)</emphasis> or
2852 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2853 these type signatures are perfectly OK
2856 g :: Ord (T a ()) => ...
2860 GHC imposes the following restrictions on the constraints in a type signature.
2864 forall tv1..tvn (c1, ...,cn) => type
2867 (Here, we write the "foralls" explicitly, although the Haskell source
2868 language omits them; in Haskell 98, all the free type variables of an
2869 explicit source-language type signature are universally quantified,
2870 except for the class type variables in a class declaration. However,
2871 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2880 <emphasis>Each universally quantified type variable
2881 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2883 A type variable <literal>a</literal> is "reachable" if it it appears
2884 in the same constraint as either a type variable free in in
2885 <literal>type</literal>, or another reachable type variable.
2886 A value with a type that does not obey
2887 this reachability restriction cannot be used without introducing
2888 ambiguity; that is why the type is rejected.
2889 Here, for example, is an illegal type:
2893 forall a. Eq a => Int
2897 When a value with this type was used, the constraint <literal>Eq tv</literal>
2898 would be introduced where <literal>tv</literal> is a fresh type variable, and
2899 (in the dictionary-translation implementation) the value would be
2900 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2901 can never know which instance of <literal>Eq</literal> to use because we never
2902 get any more information about <literal>tv</literal>.
2906 that the reachability condition is weaker than saying that <literal>a</literal> is
2907 functionally dependent on a type variable free in
2908 <literal>type</literal> (see <xref
2909 linkend="functional-dependencies"/>). The reason for this is there
2910 might be a "hidden" dependency, in a superclass perhaps. So
2911 "reachable" is a conservative approximation to "functionally dependent".
2912 For example, consider:
2914 class C a b | a -> b where ...
2915 class C a b => D a b where ...
2916 f :: forall a b. D a b => a -> a
2918 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2919 but that is not immediately apparent from <literal>f</literal>'s type.
2925 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2926 universally quantified type variables <literal>tvi</literal></emphasis>.
2928 For example, this type is OK because <literal>C a b</literal> mentions the
2929 universally quantified type variable <literal>b</literal>:
2933 forall a. C a b => burble
2937 The next type is illegal because the constraint <literal>Eq b</literal> does not
2938 mention <literal>a</literal>:
2942 forall a. Eq b => burble
2946 The reason for this restriction is milder than the other one. The
2947 excluded types are never useful or necessary (because the offending
2948 context doesn't need to be witnessed at this point; it can be floated
2949 out). Furthermore, floating them out increases sharing. Lastly,
2950 excluding them is a conservative choice; it leaves a patch of
2951 territory free in case we need it later.
2965 <sect2 id="implicit-parameters">
2966 <title>Implicit parameters</title>
2968 <para> Implicit parameters are implemented as described in
2969 "Implicit parameters: dynamic scoping with static types",
2970 J Lewis, MB Shields, E Meijer, J Launchbury,
2971 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2975 <para>(Most of the following, stil rather incomplete, documentation is
2976 due to Jeff Lewis.)</para>
2978 <para>Implicit parameter support is enabled with the option
2979 <option>-fimplicit-params</option>.</para>
2982 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2983 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2984 context. In Haskell, all variables are statically bound. Dynamic
2985 binding of variables is a notion that goes back to Lisp, but was later
2986 discarded in more modern incarnations, such as Scheme. Dynamic binding
2987 can be very confusing in an untyped language, and unfortunately, typed
2988 languages, in particular Hindley-Milner typed languages like Haskell,
2989 only support static scoping of variables.
2992 However, by a simple extension to the type class system of Haskell, we
2993 can support dynamic binding. Basically, we express the use of a
2994 dynamically bound variable as a constraint on the type. These
2995 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2996 function uses a dynamically-bound variable <literal>?x</literal>
2997 of type <literal>t'</literal>". For
2998 example, the following expresses the type of a sort function,
2999 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3001 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3003 The dynamic binding constraints are just a new form of predicate in the type class system.
3006 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3007 where <literal>x</literal> is
3008 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3009 Use of this construct also introduces a new
3010 dynamic-binding constraint in the type of the expression.
3011 For example, the following definition
3012 shows how we can define an implicitly parameterized sort function in
3013 terms of an explicitly parameterized <literal>sortBy</literal> function:
3015 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3017 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3023 <title>Implicit-parameter type constraints</title>
3025 Dynamic binding constraints behave just like other type class
3026 constraints in that they are automatically propagated. Thus, when a
3027 function is used, its implicit parameters are inherited by the
3028 function that called it. For example, our <literal>sort</literal> function might be used
3029 to pick out the least value in a list:
3031 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3032 least xs = head (sort xs)
3034 Without lifting a finger, the <literal>?cmp</literal> parameter is
3035 propagated to become a parameter of <literal>least</literal> as well. With explicit
3036 parameters, the default is that parameters must always be explicit
3037 propagated. With implicit parameters, the default is to always
3041 An implicit-parameter type constraint differs from other type class constraints in the
3042 following way: All uses of a particular implicit parameter must have
3043 the same type. This means that the type of <literal>(?x, ?x)</literal>
3044 is <literal>(?x::a) => (a,a)</literal>, and not
3045 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3049 <para> You can't have an implicit parameter in the context of a class or instance
3050 declaration. For example, both these declarations are illegal:
3052 class (?x::Int) => C a where ...
3053 instance (?x::a) => Foo [a] where ...
3055 Reason: exactly which implicit parameter you pick up depends on exactly where
3056 you invoke a function. But the ``invocation'' of instance declarations is done
3057 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3058 Easiest thing is to outlaw the offending types.</para>
3060 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3062 f :: (?x :: [a]) => Int -> Int
3065 g :: (Read a, Show a) => String -> String
3068 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3069 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3070 quite unambiguous, and fixes the type <literal>a</literal>.
3075 <title>Implicit-parameter bindings</title>
3078 An implicit parameter is <emphasis>bound</emphasis> using the standard
3079 <literal>let</literal> or <literal>where</literal> binding forms.
3080 For example, we define the <literal>min</literal> function by binding
3081 <literal>cmp</literal>.
3084 min = let ?cmp = (<=) in least
3088 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3089 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3090 (including in a list comprehension, or do-notation, or pattern guards),
3091 or a <literal>where</literal> clause.
3092 Note the following points:
3095 An implicit-parameter binding group must be a
3096 collection of simple bindings to implicit-style variables (no
3097 function-style bindings, and no type signatures); these bindings are
3098 neither polymorphic or recursive.
3101 You may not mix implicit-parameter bindings with ordinary bindings in a
3102 single <literal>let</literal>
3103 expression; use two nested <literal>let</literal>s instead.
3104 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3108 You may put multiple implicit-parameter bindings in a
3109 single binding group; but they are <emphasis>not</emphasis> treated
3110 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3111 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3112 parameter. The bindings are not nested, and may be re-ordered without changing
3113 the meaning of the program.
3114 For example, consider:
3116 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3118 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3119 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3121 f :: (?x::Int) => Int -> Int
3129 <sect3><title>Implicit parameters and polymorphic recursion</title>
3132 Consider these two definitions:
3135 len1 xs = let ?acc = 0 in len_acc1 xs
3138 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3143 len2 xs = let ?acc = 0 in len_acc2 xs
3145 len_acc2 :: (?acc :: Int) => [a] -> Int
3147 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3149 The only difference between the two groups is that in the second group
3150 <literal>len_acc</literal> is given a type signature.
3151 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3152 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3153 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3154 has a type signature, the recursive call is made to the
3155 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3156 as an implicit parameter. So we get the following results in GHCi:
3163 Adding a type signature dramatically changes the result! This is a rather
3164 counter-intuitive phenomenon, worth watching out for.
3168 <sect3><title>Implicit parameters and monomorphism</title>
3170 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3171 Haskell Report) to implicit parameters. For example, consider:
3179 Since the binding for <literal>y</literal> falls under the Monomorphism
3180 Restriction it is not generalised, so the type of <literal>y</literal> is
3181 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3182 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3183 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3184 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3185 <literal>y</literal> in the body of the <literal>let</literal> will see the
3186 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3187 <literal>14</literal>.
3192 <!-- ======================= COMMENTED OUT ========================
3194 We intend to remove linear implicit parameters, so I'm at least removing
3195 them from the 6.6 user manual
3197 <sect2 id="linear-implicit-parameters">
3198 <title>Linear implicit parameters</title>
3200 Linear implicit parameters are an idea developed by Koen Claessen,
3201 Mark Shields, and Simon PJ. They address the long-standing
3202 problem that monads seem over-kill for certain sorts of problem, notably:
3205 <listitem> <para> distributing a supply of unique names </para> </listitem>
3206 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3207 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3211 Linear implicit parameters are just like ordinary implicit parameters,
3212 except that they are "linear"; that is, they cannot be copied, and
3213 must be explicitly "split" instead. Linear implicit parameters are
3214 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3215 (The '/' in the '%' suggests the split!)
3220 import GHC.Exts( Splittable )
3222 data NameSupply = ...
3224 splitNS :: NameSupply -> (NameSupply, NameSupply)
3225 newName :: NameSupply -> Name
3227 instance Splittable NameSupply where
3231 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3232 f env (Lam x e) = Lam x' (f env e)
3235 env' = extend env x x'
3236 ...more equations for f...
3238 Notice that the implicit parameter %ns is consumed
3240 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3241 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3245 So the translation done by the type checker makes
3246 the parameter explicit:
3248 f :: NameSupply -> Env -> Expr -> Expr
3249 f ns env (Lam x e) = Lam x' (f ns1 env e)
3251 (ns1,ns2) = splitNS ns
3253 env = extend env x x'
3255 Notice the call to 'split' introduced by the type checker.
3256 How did it know to use 'splitNS'? Because what it really did
3257 was to introduce a call to the overloaded function 'split',
3258 defined by the class <literal>Splittable</literal>:
3260 class Splittable a where
3263 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3264 split for name supplies. But we can simply write
3270 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3272 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3273 <literal>GHC.Exts</literal>.
3278 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3279 are entirely distinct implicit parameters: you
3280 can use them together and they won't intefere with each other. </para>
3283 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3285 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3286 in the context of a class or instance declaration. </para></listitem>
3290 <sect3><title>Warnings</title>
3293 The monomorphism restriction is even more important than usual.
3294 Consider the example above:
3296 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3297 f env (Lam x e) = Lam x' (f env e)
3300 env' = extend env x x'
3302 If we replaced the two occurrences of x' by (newName %ns), which is
3303 usually a harmless thing to do, we get:
3305 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3306 f env (Lam x e) = Lam (newName %ns) (f env e)
3308 env' = extend env x (newName %ns)
3310 But now the name supply is consumed in <emphasis>three</emphasis> places
3311 (the two calls to newName,and the recursive call to f), so
3312 the result is utterly different. Urk! We don't even have
3316 Well, this is an experimental change. With implicit
3317 parameters we have already lost beta reduction anyway, and
3318 (as John Launchbury puts it) we can't sensibly reason about
3319 Haskell programs without knowing their typing.
3324 <sect3><title>Recursive functions</title>
3325 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3328 foo :: %x::T => Int -> [Int]
3330 foo n = %x : foo (n-1)
3332 where T is some type in class Splittable.</para>
3334 Do you get a list of all the same T's or all different T's
3335 (assuming that split gives two distinct T's back)?
3337 If you supply the type signature, taking advantage of polymorphic
3338 recursion, you get what you'd probably expect. Here's the
3339 translated term, where the implicit param is made explicit:
3342 foo x n = let (x1,x2) = split x
3343 in x1 : foo x2 (n-1)
3345 But if you don't supply a type signature, GHC uses the Hindley
3346 Milner trick of using a single monomorphic instance of the function
3347 for the recursive calls. That is what makes Hindley Milner type inference
3348 work. So the translation becomes
3352 foom n = x : foom (n-1)
3356 Result: 'x' is not split, and you get a list of identical T's. So the
3357 semantics of the program depends on whether or not foo has a type signature.
3360 You may say that this is a good reason to dislike linear implicit parameters
3361 and you'd be right. That is why they are an experimental feature.
3367 ================ END OF Linear Implicit Parameters commented out -->
3369 <sect2 id="kinding">
3370 <title>Explicitly-kinded quantification</title>
3373 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3374 to give the kind explicitly as (machine-checked) documentation,
3375 just as it is nice to give a type signature for a function. On some occasions,
3376 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3377 John Hughes had to define the data type:
3379 data Set cxt a = Set [a]
3380 | Unused (cxt a -> ())
3382 The only use for the <literal>Unused</literal> constructor was to force the correct
3383 kind for the type variable <literal>cxt</literal>.
3386 GHC now instead allows you to specify the kind of a type variable directly, wherever
3387 a type variable is explicitly bound. Namely:
3389 <listitem><para><literal>data</literal> declarations:
3391 data Set (cxt :: * -> *) a = Set [a]
3392 </screen></para></listitem>
3393 <listitem><para><literal>type</literal> declarations:
3395 type T (f :: * -> *) = f Int
3396 </screen></para></listitem>
3397 <listitem><para><literal>class</literal> declarations:
3399 class (Eq a) => C (f :: * -> *) a where ...
3400 </screen></para></listitem>
3401 <listitem><para><literal>forall</literal>'s in type signatures:
3403 f :: forall (cxt :: * -> *). Set cxt Int
3404 </screen></para></listitem>
3409 The parentheses are required. Some of the spaces are required too, to
3410 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3411 will get a parse error, because "<literal>::*->*</literal>" is a
3412 single lexeme in Haskell.
3416 As part of the same extension, you can put kind annotations in types
3419 f :: (Int :: *) -> Int
3420 g :: forall a. a -> (a :: *)
3424 atype ::= '(' ctype '::' kind ')
3426 The parentheses are required.
3431 <sect2 id="universal-quantification">
3432 <title>Arbitrary-rank polymorphism
3436 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3437 allows us to say exactly what this means. For example:
3445 g :: forall b. (b -> b)
3447 The two are treated identically.
3451 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3452 explicit universal quantification in
3454 For example, all the following types are legal:
3456 f1 :: forall a b. a -> b -> a
3457 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3459 f2 :: (forall a. a->a) -> Int -> Int
3460 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3462 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3464 f4 :: Int -> (forall a. a -> a)
3466 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3467 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3468 The <literal>forall</literal> makes explicit the universal quantification that
3469 is implicitly added by Haskell.
3472 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3473 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3474 shows, the polymorphic type on the left of the function arrow can be overloaded.
3477 The function <literal>f3</literal> has a rank-3 type;
3478 it has rank-2 types on the left of a function arrow.
3481 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3482 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3483 that restriction has now been lifted.)
3484 In particular, a forall-type (also called a "type scheme"),
3485 including an operational type class context, is legal:
3487 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3488 of a function arrow </para> </listitem>
3489 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3490 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3491 field type signatures.</para> </listitem>
3492 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3493 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3495 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3496 a type variable any more!
3505 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3506 the types of the constructor arguments. Here are several examples:
3512 data T a = T1 (forall b. b -> b -> b) a
3514 data MonadT m = MkMonad { return :: forall a. a -> m a,
3515 bind :: forall a b. m a -> (a -> m b) -> m b
3518 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3524 The constructors have rank-2 types:
3530 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3531 MkMonad :: forall m. (forall a. a -> m a)
3532 -> (forall a b. m a -> (a -> m b) -> m b)
3534 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3540 Notice that you don't need to use a <literal>forall</literal> if there's an
3541 explicit context. For example in the first argument of the
3542 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3543 prefixed to the argument type. The implicit <literal>forall</literal>
3544 quantifies all type variables that are not already in scope, and are
3545 mentioned in the type quantified over.
3549 As for type signatures, implicit quantification happens for non-overloaded
3550 types too. So if you write this:
3553 data T a = MkT (Either a b) (b -> b)
3556 it's just as if you had written this:
3559 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3562 That is, since the type variable <literal>b</literal> isn't in scope, it's
3563 implicitly universally quantified. (Arguably, it would be better
3564 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3565 where that is what is wanted. Feedback welcomed.)
3569 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3570 the constructor to suitable values, just as usual. For example,
3581 a3 = MkSwizzle reverse
3584 a4 = let r x = Just x
3591 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3592 mkTs f x y = [T1 f x, T1 f y]
3598 The type of the argument can, as usual, be more general than the type
3599 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3600 does not need the <literal>Ord</literal> constraint.)
3604 When you use pattern matching, the bound variables may now have
3605 polymorphic types. For example:
3611 f :: T a -> a -> (a, Char)
3612 f (T1 w k) x = (w k x, w 'c' 'd')
3614 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3615 g (MkSwizzle s) xs f = s (map f (s xs))
3617 h :: MonadT m -> [m a] -> m [a]
3618 h m [] = return m []
3619 h m (x:xs) = bind m x $ \y ->
3620 bind m (h m xs) $ \ys ->
3627 In the function <function>h</function> we use the record selectors <literal>return</literal>
3628 and <literal>bind</literal> to extract the polymorphic bind and return functions
3629 from the <literal>MonadT</literal> data structure, rather than using pattern
3635 <title>Type inference</title>
3638 In general, type inference for arbitrary-rank types is undecidable.
3639 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3640 to get a decidable algorithm by requiring some help from the programmer.
3641 We do not yet have a formal specification of "some help" but the rule is this:
3644 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3645 provides an explicit polymorphic type for x, or GHC's type inference will assume
3646 that x's type has no foralls in it</emphasis>.
3649 What does it mean to "provide" an explicit type for x? You can do that by
3650 giving a type signature for x directly, using a pattern type signature
3651 (<xref linkend="scoped-type-variables"/>), thus:
3653 \ f :: (forall a. a->a) -> (f True, f 'c')
3655 Alternatively, you can give a type signature to the enclosing
3656 context, which GHC can "push down" to find the type for the variable:
3658 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3660 Here the type signature on the expression can be pushed inwards
3661 to give a type signature for f. Similarly, and more commonly,
3662 one can give a type signature for the function itself:
3664 h :: (forall a. a->a) -> (Bool,Char)
3665 h f = (f True, f 'c')
3667 You don't need to give a type signature if the lambda bound variable
3668 is a constructor argument. Here is an example we saw earlier:
3670 f :: T a -> a -> (a, Char)
3671 f (T1 w k) x = (w k x, w 'c' 'd')
3673 Here we do not need to give a type signature to <literal>w</literal>, because
3674 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3681 <sect3 id="implicit-quant">
3682 <title>Implicit quantification</title>
3685 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3686 user-written types, if and only if there is no explicit <literal>forall</literal>,
3687 GHC finds all the type variables mentioned in the type that are not already
3688 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3692 f :: forall a. a -> a
3699 h :: forall b. a -> b -> b
3705 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3708 f :: (a -> a) -> Int
3710 f :: forall a. (a -> a) -> Int
3712 f :: (forall a. a -> a) -> Int
3715 g :: (Ord a => a -> a) -> Int
3716 -- MEANS the illegal type
3717 g :: forall a. (Ord a => a -> a) -> Int
3719 g :: (forall a. Ord a => a -> a) -> Int
3721 The latter produces an illegal type, which you might think is silly,
3722 but at least the rule is simple. If you want the latter type, you
3723 can write your for-alls explicitly. Indeed, doing so is strongly advised
3730 <sect2 id="impredicative-polymorphism">
3731 <title>Impredicative polymorphism
3733 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3734 that you can call a polymorphic function at a polymorphic type, and
3735 parameterise data structures over polymorphic types. For example:
3737 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3738 f (Just g) = Just (g [3], g "hello")
3741 Notice here that the <literal>Maybe</literal> type is parameterised by the
3742 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3745 <para>The technical details of this extension are described in the paper
3746 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3747 type inference for higher-rank types and impredicativity</ulink>,
3748 which appeared at ICFP 2006.
3752 <sect2 id="scoped-type-variables">
3753 <title>Lexically scoped type variables
3757 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3758 which some type signatures are simply impossible to write. For example:
3760 f :: forall a. [a] -> [a]
3766 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3767 the entire definition of <literal>f</literal>.
3768 In particular, it is in scope at the type signature for <varname>ys</varname>.
3769 In Haskell 98 it is not possible to declare
3770 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3771 it becomes possible to do so.
3773 <para>Lexically-scoped type variables are enabled by
3774 <option>-fglasgow-exts</option>.
3776 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3777 variables work, compared to earlier releases. Read this section
3781 <title>Overview</title>
3783 <para>The design follows the following principles
3785 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3786 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3787 design.)</para></listitem>
3788 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3789 type variables. This means that every programmer-written type signature
3790 (includin one that contains free scoped type variables) denotes a
3791 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3792 checker, and no inference is involved.</para></listitem>
3793 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3794 changing the program.</para></listitem>
3798 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3800 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3801 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3802 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3803 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3807 In Haskell, a programmer-written type signature is implicitly quantifed over
3808 its free type variables (<ulink
3809 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3811 of the Haskel Report).
3812 Lexically scoped type variables affect this implicit quantification rules
3813 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3814 quantified. For example, if type variable <literal>a</literal> is in scope,
3817 (e :: a -> a) means (e :: a -> a)
3818 (e :: b -> b) means (e :: forall b. b->b)
3819 (e :: a -> b) means (e :: forall b. a->b)
3827 <sect3 id="decl-type-sigs">
3828 <title>Declaration type signatures</title>
3829 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3830 quantification (using <literal>forall</literal>) brings into scope the
3831 explicitly-quantified
3832 type variables, in the definition of the named function(s). For example:
3834 f :: forall a. [a] -> [a]
3835 f (x:xs) = xs ++ [ x :: a ]
3837 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3838 the definition of "<literal>f</literal>".
3840 <para>This only happens if the quantification in <literal>f</literal>'s type
3841 signature is explicit. For example:
3844 g (x:xs) = xs ++ [ x :: a ]
3846 This program will be rejected, because "<literal>a</literal>" does not scope
3847 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3848 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3849 quantification rules.
3853 <sect3 id="exp-type-sigs">
3854 <title>Expression type signatures</title>
3856 <para>An expression type signature that has <emphasis>explicit</emphasis>
3857 quantification (using <literal>forall</literal>) brings into scope the
3858 explicitly-quantified
3859 type variables, in the annotated expression. For example:
3861 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3863 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3864 type variable <literal>s</literal> into scope, in the annotated expression
3865 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3870 <sect3 id="pattern-type-sigs">
3871 <title>Pattern type signatures</title>
3873 A type signature may occur in any pattern; this is a <emphasis>pattern type
3874 signature</emphasis>.
3877 -- f and g assume that 'a' is already in scope
3878 f = \(x::Int, y::a) -> x
3880 h ((x,y) :: (Int,Bool)) = (y,x)
3882 In the case where all the type variables in the pattern type sigature are
3883 already in scope (i.e. bound by the enclosing context), matters are simple: the
3884 signature simply constrains the type of the pattern in the obvious way.
3887 There is only one situation in which you can write a pattern type signature that
3888 mentions a type variable that is not already in scope, namely in pattern match
3889 of an existential data constructor. For example:
3891 data T = forall a. MkT [a]
3894 k (MkT [t::a]) = MkT t3
3898 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3899 variable that is not already in scope. Indeed, it cannot already be in scope,
3900 because it is bound by the pattern match. GHC's rule is that in this situation
3901 (and only then), a pattern type signature can mention a type variable that is
3902 not already in scope; the effect is to bring it into scope, standing for the
3903 existentially-bound type variable.
3906 If this seems a little odd, we think so too. But we must have
3907 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3908 could not name existentially-bound type variables in subequent type signatures.
3911 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3912 signature is allowed to mention a lexical variable that is not already in
3914 For example, both <literal>f</literal> and <literal>g</literal> would be
3915 illegal if <literal>a</literal> was not already in scope.
3921 <!-- ==================== Commented out part about result type signatures
3923 <sect3 id="result-type-sigs">
3924 <title>Result type signatures</title>
3927 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3930 {- f assumes that 'a' is already in scope -}
3931 f x y :: [a] = [x,y,x]
3933 g = \ x :: [Int] -> [3,4]
3935 h :: forall a. [a] -> a
3939 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3940 the result of the function. Similarly, the body of the lambda in the RHS of
3941 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3942 alternative in <literal>h</literal> is <literal>a</literal>.
3944 <para> A result type signature never brings new type variables into scope.</para>
3946 There are a couple of syntactic wrinkles. First, notice that all three
3947 examples would parse quite differently with parentheses:
3949 {- f assumes that 'a' is already in scope -}
3950 f x (y :: [a]) = [x,y,x]
3952 g = \ (x :: [Int]) -> [3,4]
3954 h :: forall a. [a] -> a
3958 Now the signature is on the <emphasis>pattern</emphasis>; and
3959 <literal>h</literal> would certainly be ill-typed (since the pattern
3960 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3962 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3963 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3964 token or a parenthesised type of some sort). To see why,
3965 consider how one would parse this:
3974 <sect3 id="cls-inst-scoped-tyvars">
3975 <title>Class and instance declarations</title>
3978 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3979 scope over the methods defined in the <literal>where</literal> part. For example:
3997 <sect2 id="typing-binds">
3998 <title>Generalised typing of mutually recursive bindings</title>
4001 The Haskell Report specifies that a group of bindings (at top level, or in a
4002 <literal>let</literal> or <literal>where</literal>) should be sorted into
4003 strongly-connected components, and then type-checked in dependency order
4004 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4005 Report, Section 4.5.1</ulink>).
4006 As each group is type-checked, any binders of the group that
4008 an explicit type signature are put in the type environment with the specified
4010 and all others are monomorphic until the group is generalised
4011 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4014 <para>Following a suggestion of Mark Jones, in his paper
4015 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4017 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
4019 <emphasis>the dependency analysis ignores references to variables that have an explicit
4020 type signature</emphasis>.
4021 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4022 typecheck. For example, consider:
4024 f :: Eq a => a -> Bool
4025 f x = (x == x) || g True || g "Yes"
4027 g y = (y <= y) || f True
4029 This is rejected by Haskell 98, but under Jones's scheme the definition for
4030 <literal>g</literal> is typechecked first, separately from that for
4031 <literal>f</literal>,
4032 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4033 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4034 type is generalised, to get
4036 g :: Ord a => a -> Bool
4038 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4039 <literal>g</literal> in the type environment.
4043 The same refined dependency analysis also allows the type signatures of
4044 mutually-recursive functions to have different contexts, something that is illegal in
4045 Haskell 98 (Section 4.5.2, last sentence). With
4046 <option>-fglasgow-exts</option>
4047 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4048 type signatures; in practice this means that only variables bound by the same
4049 pattern binding must have the same context. For example, this is fine:
4051 f :: Eq a => a -> Bool
4052 f x = (x == x) || g True
4054 g :: Ord a => a -> Bool
4055 g y = (y <= y) || f True
4060 <sect2 id="overloaded-strings">
4061 <title>Overloaded string literals
4065 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4066 string literal has type <literal>String</literal>, but with overloaded string
4067 literals enabled (with <literal>-foverloaded-strings</literal>)
4068 a string literal has type <literal>(IsString a) => a</literal>.
4071 This means that the usual string syntax can be used, e.g., for packed strings
4072 and other variations of string like types. String literals behave very much
4073 like integer literals, i.e., they can be used in both expressions and patterns.
4074 If used in a pattern the literal with be replaced by an equality test, in the same
4075 way as an integer literal is.
4078 The class <literal>IsString</literal> is defined as:
4080 class IsString a where
4081 fromString :: String -> a
4083 The only predefined instance is the obvious one to make strings work as usual:
4085 instance IsString [Char] where
4088 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4089 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4090 from module <literal>GHC.Exts</literal>.
4093 Haskell's defaulting mechanism is extended to cover string literals, when <option>-foverloaded-strings</option> is specified.
4097 Each type in a default declaration must be an
4098 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4102 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4103 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4104 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4105 <emphasis>or</emphasis> <literal>IsString</literal>.
4114 import GHC.Exts( IsString(..) )
4116 newtype MyString = MyString String deriving (Eq, Show)
4117 instance IsString MyString where
4118 fromString = MyString
4120 greet :: MyString -> MyString
4121 greet "hello" = "world"
4125 print $ greet "hello"
4126 print $ greet "fool"
4130 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4131 to work since it gets translated into an equality comparison.
4136 <!-- ==================== End of type system extensions ================= -->
4138 <!-- ====================== TEMPLATE HASKELL ======================= -->
4140 <sect1 id="template-haskell">
4141 <title>Template Haskell</title>
4143 <para>Template Haskell allows you to do compile-time meta-programming in
4146 the main technical innovations is discussed in "<ulink
4147 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4148 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4151 There is a Wiki page about
4152 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4153 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4157 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4158 Haskell library reference material</ulink>
4159 (search for the type ExpQ).
4160 [Temporary: many changes to the original design are described in
4161 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4162 Not all of these changes are in GHC 6.6.]
4165 <para> The first example from that paper is set out below as a worked example to help get you started.
4169 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4170 Tim Sheard is going to expand it.)
4174 <title>Syntax</title>
4176 <para> Template Haskell has the following new syntactic
4177 constructions. You need to use the flag
4178 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4179 </indexterm>to switch these syntactic extensions on
4180 (<option>-fth</option> is no longer implied by
4181 <option>-fglasgow-exts</option>).</para>
4185 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4186 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4187 There must be no space between the "$" and the identifier or parenthesis. This use
4188 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4189 of "." as an infix operator. If you want the infix operator, put spaces around it.
4191 <para> A splice can occur in place of
4193 <listitem><para> an expression; the spliced expression must
4194 have type <literal>Q Exp</literal></para></listitem>
4195 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4196 <listitem><para> [Planned, but not implemented yet.] a
4197 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4199 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4200 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4206 A expression quotation is written in Oxford brackets, thus:
4208 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4209 the quotation has type <literal>Expr</literal>.</para></listitem>
4210 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4211 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4212 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4213 the quotation has type <literal>Type</literal>.</para></listitem>
4214 </itemizedlist></para></listitem>
4217 Reification is written thus:
4219 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4220 has type <literal>Dec</literal>. </para></listitem>
4221 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4222 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4223 <listitem><para> Still to come: fixities </para></listitem>
4225 </itemizedlist></para>
4232 <sect2> <title> Using Template Haskell </title>
4236 The data types and monadic constructor functions for Template Haskell are in the library
4237 <literal>Language.Haskell.THSyntax</literal>.
4241 You can only run a function at compile time if it is imported from another module. That is,
4242 you can't define a function in a module, and call it from within a splice in the same module.
4243 (It would make sense to do so, but it's hard to implement.)
4247 Furthermore, you can only run a function at compile time if it is imported
4248 from another module <emphasis>that is not part of a mutually-recursive group of modules
4249 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4250 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4251 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4255 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4258 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4259 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4260 compiles and runs a program, and then looks at the result. So it's important that
4261 the program it compiles produces results whose representations are identical to
4262 those of the compiler itself.
4266 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4267 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4272 <sect2> <title> A Template Haskell Worked Example </title>
4273 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4274 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4281 -- Import our template "pr"
4282 import Printf ( pr )
4284 -- The splice operator $ takes the Haskell source code
4285 -- generated at compile time by "pr" and splices it into
4286 -- the argument of "putStrLn".
4287 main = putStrLn ( $(pr "Hello") )
4293 -- Skeletal printf from the paper.
4294 -- It needs to be in a separate module to the one where
4295 -- you intend to use it.
4297 -- Import some Template Haskell syntax
4298 import Language.Haskell.TH
4300 -- Describe a format string
4301 data Format = D | S | L String
4303 -- Parse a format string. This is left largely to you
4304 -- as we are here interested in building our first ever
4305 -- Template Haskell program and not in building printf.
4306 parse :: String -> [Format]
4309 -- Generate Haskell source code from a parsed representation
4310 -- of the format string. This code will be spliced into
4311 -- the module which calls "pr", at compile time.
4312 gen :: [Format] -> ExpQ
4313 gen [D] = [| \n -> show n |]
4314 gen [S] = [| \s -> s |]
4315 gen [L s] = stringE s
4317 -- Here we generate the Haskell code for the splice
4318 -- from an input format string.
4319 pr :: String -> ExpQ
4320 pr s = gen (parse s)
4323 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4326 $ ghc --make -fth main.hs -o main.exe
4329 <para>Run "main.exe" and here is your output:</para>
4339 <title>Using Template Haskell with Profiling</title>
4340 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4342 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4343 interpreter to run the splice expressions. The bytecode interpreter
4344 runs the compiled expression on top of the same runtime on which GHC
4345 itself is running; this means that the compiled code referred to by
4346 the interpreted expression must be compatible with this runtime, and
4347 in particular this means that object code that is compiled for
4348 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4349 expression, because profiled object code is only compatible with the
4350 profiling version of the runtime.</para>
4352 <para>This causes difficulties if you have a multi-module program
4353 containing Template Haskell code and you need to compile it for
4354 profiling, because GHC cannot load the profiled object code and use it
4355 when executing the splices. Fortunately GHC provides a workaround.
4356 The basic idea is to compile the program twice:</para>
4360 <para>Compile the program or library first the normal way, without
4361 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4364 <para>Then compile it again with <option>-prof</option>, and
4365 additionally use <option>-osuf
4366 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4367 to name the object files differentliy (you can choose any suffix
4368 that isn't the normal object suffix here). GHC will automatically
4369 load the object files built in the first step when executing splice
4370 expressions. If you omit the <option>-osuf</option> flag when
4371 building with <option>-prof</option> and Template Haskell is used,
4372 GHC will emit an error message. </para>
4379 <!-- ===================== Arrow notation =================== -->
4381 <sect1 id="arrow-notation">
4382 <title>Arrow notation
4385 <para>Arrows are a generalization of monads introduced by John Hughes.
4386 For more details, see
4391 “Generalising Monads to Arrows”,
4392 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4393 pp67–111, May 2000.
4399 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4400 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4406 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4407 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4413 and the arrows web page at
4414 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4415 With the <option>-farrows</option> flag, GHC supports the arrow
4416 notation described in the second of these papers.
4417 What follows is a brief introduction to the notation;
4418 it won't make much sense unless you've read Hughes's paper.
4419 This notation is translated to ordinary Haskell,
4420 using combinators from the
4421 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4425 <para>The extension adds a new kind of expression for defining arrows:
4427 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4428 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4430 where <literal>proc</literal> is a new keyword.
4431 The variables of the pattern are bound in the body of the
4432 <literal>proc</literal>-expression,
4433 which is a new sort of thing called a <firstterm>command</firstterm>.
4434 The syntax of commands is as follows:
4436 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4437 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4438 | <replaceable>cmd</replaceable><superscript>0</superscript>
4440 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4441 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4442 infix operators as for expressions, and
4444 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4445 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4446 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4447 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4448 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4449 | <replaceable>fcmd</replaceable>
4451 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4452 | ( <replaceable>cmd</replaceable> )
4453 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4455 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4456 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4457 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4458 | <replaceable>cmd</replaceable>
4460 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4461 except that the bodies are commands instead of expressions.
4465 Commands produce values, but (like monadic computations)
4466 may yield more than one value,
4467 or none, and may do other things as well.
4468 For the most part, familiarity with monadic notation is a good guide to
4470 However the values of expressions, even monadic ones,
4471 are determined by the values of the variables they contain;
4472 this is not necessarily the case for commands.
4476 A simple example of the new notation is the expression
4478 proc x -> f -< x+1
4480 We call this a <firstterm>procedure</firstterm> or
4481 <firstterm>arrow abstraction</firstterm>.
4482 As with a lambda expression, the variable <literal>x</literal>
4483 is a new variable bound within the <literal>proc</literal>-expression.
4484 It refers to the input to the arrow.
4485 In the above example, <literal>-<</literal> is not an identifier but an
4486 new reserved symbol used for building commands from an expression of arrow
4487 type and an expression to be fed as input to that arrow.
4488 (The weird look will make more sense later.)
4489 It may be read as analogue of application for arrows.
4490 The above example is equivalent to the Haskell expression
4492 arr (\ x -> x+1) >>> f
4494 That would make no sense if the expression to the left of
4495 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4496 More generally, the expression to the left of <literal>-<</literal>
4497 may not involve any <firstterm>local variable</firstterm>,
4498 i.e. a variable bound in the current arrow abstraction.
4499 For such a situation there is a variant <literal>-<<</literal>, as in
4501 proc x -> f x -<< x+1
4503 which is equivalent to
4505 arr (\ x -> (f x, x+1)) >>> app
4507 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4509 Such an arrow is equivalent to a monad, so if you're using this form
4510 you may find a monadic formulation more convenient.
4514 <title>do-notation for commands</title>
4517 Another form of command is a form of <literal>do</literal>-notation.
4518 For example, you can write
4527 You can read this much like ordinary <literal>do</literal>-notation,
4528 but with commands in place of monadic expressions.
4529 The first line sends the value of <literal>x+1</literal> as an input to
4530 the arrow <literal>f</literal>, and matches its output against
4531 <literal>y</literal>.
4532 In the next line, the output is discarded.
4533 The arrow <function>returnA</function> is defined in the
4534 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4535 module as <literal>arr id</literal>.
4536 The above example is treated as an abbreviation for
4538 arr (\ x -> (x, x)) >>>
4539 first (arr (\ x -> x+1) >>> f) >>>
4540 arr (\ (y, x) -> (y, (x, y))) >>>
4541 first (arr (\ y -> 2*y) >>> g) >>>
4543 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4544 first (arr (\ (x, z) -> x*z) >>> h) >>>
4545 arr (\ (t, z) -> t+z) >>>
4548 Note that variables not used later in the composition are projected out.
4549 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4551 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4552 module, this reduces to
4554 arr (\ x -> (x+1, x)) >>>
4556 arr (\ (y, x) -> (2*y, (x, y))) >>>
4558 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4560 arr (\ (t, z) -> t+z)
4562 which is what you might have written by hand.
4563 With arrow notation, GHC keeps track of all those tuples of variables for you.
4567 Note that although the above translation suggests that
4568 <literal>let</literal>-bound variables like <literal>z</literal> must be
4569 monomorphic, the actual translation produces Core,
4570 so polymorphic variables are allowed.
4574 It's also possible to have mutually recursive bindings,
4575 using the new <literal>rec</literal> keyword, as in the following example:
4577 counter :: ArrowCircuit a => a Bool Int
4578 counter = proc reset -> do
4579 rec output <- returnA -< if reset then 0 else next
4580 next <- delay 0 -< output+1
4581 returnA -< output
4583 The translation of such forms uses the <function>loop</function> combinator,
4584 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4590 <title>Conditional commands</title>
4593 In the previous example, we used a conditional expression to construct the
4595 Sometimes we want to conditionally execute different commands, as in
4602 which is translated to
4604 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4605 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4607 Since the translation uses <function>|||</function>,
4608 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4612 There are also <literal>case</literal> commands, like
4618 y <- h -< (x1, x2)
4622 The syntax is the same as for <literal>case</literal> expressions,
4623 except that the bodies of the alternatives are commands rather than expressions.
4624 The translation is similar to that of <literal>if</literal> commands.
4630 <title>Defining your own control structures</title>
4633 As we're seen, arrow notation provides constructs,
4634 modelled on those for expressions,
4635 for sequencing, value recursion and conditionals.
4636 But suitable combinators,
4637 which you can define in ordinary Haskell,
4638 may also be used to build new commands out of existing ones.
4639 The basic idea is that a command defines an arrow from environments to values.
4640 These environments assign values to the free local variables of the command.
4641 Thus combinators that produce arrows from arrows
4642 may also be used to build commands from commands.
4643 For example, the <literal>ArrowChoice</literal> class includes a combinator
4645 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4647 so we can use it to build commands:
4649 expr' = proc x -> do
4652 symbol Plus -< ()
4653 y <- term -< ()
4656 symbol Minus -< ()
4657 y <- term -< ()
4660 (The <literal>do</literal> on the first line is needed to prevent the first
4661 <literal><+> ...</literal> from being interpreted as part of the
4662 expression on the previous line.)
4663 This is equivalent to
4665 expr' = (proc x -> returnA -< x)
4666 <+> (proc x -> do
4667 symbol Plus -< ()
4668 y <- term -< ()
4670 <+> (proc x -> do
4671 symbol Minus -< ()
4672 y <- term -< ()
4675 It is essential that this operator be polymorphic in <literal>e</literal>
4676 (representing the environment input to the command
4677 and thence to its subcommands)
4678 and satisfy the corresponding naturality property
4680 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4682 at least for strict <literal>k</literal>.
4683 (This should be automatic if you're not using <function>seq</function>.)
4684 This ensures that environments seen by the subcommands are environments
4685 of the whole command,
4686 and also allows the translation to safely trim these environments.
4687 The operator must also not use any variable defined within the current
4692 We could define our own operator
4694 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4695 untilA body cond = proc x ->
4696 if cond x then returnA -< ()
4699 untilA body cond -< x
4701 and use it in the same way.
4702 Of course this infix syntax only makes sense for binary operators;
4703 there is also a more general syntax involving special brackets:
4707 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4714 <title>Primitive constructs</title>
4717 Some operators will need to pass additional inputs to their subcommands.
4718 For example, in an arrow type supporting exceptions,
4719 the operator that attaches an exception handler will wish to pass the
4720 exception that occurred to the handler.
4721 Such an operator might have a type
4723 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4725 where <literal>Ex</literal> is the type of exceptions handled.
4726 You could then use this with arrow notation by writing a command
4728 body `handleA` \ ex -> handler
4730 so that if an exception is raised in the command <literal>body</literal>,
4731 the variable <literal>ex</literal> is bound to the value of the exception
4732 and the command <literal>handler</literal>,
4733 which typically refers to <literal>ex</literal>, is entered.
4734 Though the syntax here looks like a functional lambda,
4735 we are talking about commands, and something different is going on.
4736 The input to the arrow represented by a command consists of values for
4737 the free local variables in the command, plus a stack of anonymous values.
4738 In all the prior examples, this stack was empty.
4739 In the second argument to <function>handleA</function>,
4740 this stack consists of one value, the value of the exception.
4741 The command form of lambda merely gives this value a name.
4746 the values on the stack are paired to the right of the environment.
4747 So operators like <function>handleA</function> that pass
4748 extra inputs to their subcommands can be designed for use with the notation
4749 by pairing the values with the environment in this way.
4750 More precisely, the type of each argument of the operator (and its result)
4751 should have the form
4753 a (...(e,t1), ... tn) t
4755 where <replaceable>e</replaceable> is a polymorphic variable
4756 (representing the environment)
4757 and <replaceable>ti</replaceable> are the types of the values on the stack,
4758 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4759 The polymorphic variable <replaceable>e</replaceable> must not occur in
4760 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4761 <replaceable>t</replaceable>.
4762 However the arrows involved need not be the same.
4763 Here are some more examples of suitable operators:
4765 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4766 runReader :: ... => a e c -> a' (e,State) c
4767 runState :: ... => a e c -> a' (e,State) (c,State)
4769 We can supply the extra input required by commands built with the last two
4770 by applying them to ordinary expressions, as in
4774 (|runReader (do { ... })|) s
4776 which adds <literal>s</literal> to the stack of inputs to the command
4777 built using <function>runReader</function>.
4781 The command versions of lambda abstraction and application are analogous to
4782 the expression versions.
4783 In particular, the beta and eta rules describe equivalences of commands.
4784 These three features (operators, lambda abstraction and application)
4785 are the core of the notation; everything else can be built using them,
4786 though the results would be somewhat clumsy.
4787 For example, we could simulate <literal>do</literal>-notation by defining
4789 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4790 u `bind` f = returnA &&& u >>> f
4792 bind_ :: Arrow a => a e b -> a e c -> a e c
4793 u `bind_` f = u `bind` (arr fst >>> f)
4795 We could simulate <literal>if</literal> by defining
4797 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4798 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4805 <title>Differences with the paper</title>
4810 <para>Instead of a single form of arrow application (arrow tail) with two
4811 translations, the implementation provides two forms
4812 <quote><literal>-<</literal></quote> (first-order)
4813 and <quote><literal>-<<</literal></quote> (higher-order).
4818 <para>User-defined operators are flagged with banana brackets instead of
4819 a new <literal>form</literal> keyword.
4828 <title>Portability</title>
4831 Although only GHC implements arrow notation directly,
4832 there is also a preprocessor
4834 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4835 that translates arrow notation into Haskell 98
4836 for use with other Haskell systems.
4837 You would still want to check arrow programs with GHC;
4838 tracing type errors in the preprocessor output is not easy.
4839 Modules intended for both GHC and the preprocessor must observe some
4840 additional restrictions:
4845 The module must import
4846 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4852 The preprocessor cannot cope with other Haskell extensions.
4853 These would have to go in separate modules.
4859 Because the preprocessor targets Haskell (rather than Core),
4860 <literal>let</literal>-bound variables are monomorphic.
4871 <!-- ==================== BANG PATTERNS ================= -->
4873 <sect1 id="bang-patterns">
4874 <title>Bang patterns
4875 <indexterm><primary>Bang patterns</primary></indexterm>
4877 <para>GHC supports an extension of pattern matching called <emphasis>bang
4878 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4880 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4881 prime feature description</ulink> contains more discussion and examples
4882 than the material below.
4885 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4888 <sect2 id="bang-patterns-informal">
4889 <title>Informal description of bang patterns
4892 The main idea is to add a single new production to the syntax of patterns:
4896 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4897 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4902 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4903 whereas without the bang it would be lazy.
4904 Bang patterns can be nested of course:
4908 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4909 <literal>y</literal>.
4910 A bang only really has an effect if it precedes a variable or wild-card pattern:
4915 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4916 forces evaluation anyway does nothing.
4918 Bang patterns work in <literal>case</literal> expressions too, of course:
4920 g5 x = let y = f x in body
4921 g6 x = case f x of { y -> body }
4922 g7 x = case f x of { !y -> body }
4924 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4925 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4926 result, and then evaluates <literal>body</literal>.
4928 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4929 definitions too. For example:
4933 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4934 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4935 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4936 in a function argument <literal>![x,y]</literal> means the
4937 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4938 is part of the syntax of <literal>let</literal> bindings.
4943 <sect2 id="bang-patterns-sem">
4944 <title>Syntax and semantics
4948 We add a single new production to the syntax of patterns:
4952 There is one problem with syntactic ambiguity. Consider:
4956 Is this a definition of the infix function "<literal>(!)</literal>",
4957 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4958 ambiguity in favour of the latter. If you want to define
4959 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4964 The semantics of Haskell pattern matching is described in <ulink
4965 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4966 Section 3.17.2</ulink> of the Haskell Report. To this description add
4967 one extra item 10, saying:
4968 <itemizedlist><listitem><para>Matching
4969 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4970 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4971 <listitem><para>otherwise, <literal>pat</literal> is matched against
4972 <literal>v</literal></para></listitem>
4974 </para></listitem></itemizedlist>
4975 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4976 Section 3.17.3</ulink>, add a new case (t):
4978 case v of { !pat -> e; _ -> e' }
4979 = v `seq` case v of { pat -> e; _ -> e' }
4982 That leaves let expressions, whose translation is given in
4983 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4985 of the Haskell Report.
4986 In the translation box, first apply
4987 the following transformation: for each pattern <literal>pi</literal> that is of
4988 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4989 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4990 have a bang at the top, apply the rules in the existing box.
4992 <para>The effect of the let rule is to force complete matching of the pattern
4993 <literal>qi</literal> before evaluation of the body is begun. The bang is
4994 retained in the translated form in case <literal>qi</literal> is a variable,
5002 The let-binding can be recursive. However, it is much more common for
5003 the let-binding to be non-recursive, in which case the following law holds:
5004 <literal>(let !p = rhs in body)</literal>
5006 <literal>(case rhs of !p -> body)</literal>
5009 A pattern with a bang at the outermost level is not allowed at the top level of
5015 <!-- ==================== ASSERTIONS ================= -->
5017 <sect1 id="assertions">
5019 <indexterm><primary>Assertions</primary></indexterm>
5023 If you want to make use of assertions in your standard Haskell code, you
5024 could define a function like the following:
5030 assert :: Bool -> a -> a
5031 assert False x = error "assertion failed!"
5038 which works, but gives you back a less than useful error message --
5039 an assertion failed, but which and where?
5043 One way out is to define an extended <function>assert</function> function which also
5044 takes a descriptive string to include in the error message and
5045 perhaps combine this with the use of a pre-processor which inserts
5046 the source location where <function>assert</function> was used.
5050 Ghc offers a helping hand here, doing all of this for you. For every
5051 use of <function>assert</function> in the user's source:
5057 kelvinToC :: Double -> Double
5058 kelvinToC k = assert (k >= 0.0) (k+273.15)
5064 Ghc will rewrite this to also include the source location where the
5071 assert pred val ==> assertError "Main.hs|15" pred val
5077 The rewrite is only performed by the compiler when it spots
5078 applications of <function>Control.Exception.assert</function>, so you
5079 can still define and use your own versions of
5080 <function>assert</function>, should you so wish. If not, import
5081 <literal>Control.Exception</literal> to make use
5082 <function>assert</function> in your code.
5086 GHC ignores assertions when optimisation is turned on with the
5087 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5088 <literal>assert pred e</literal> will be rewritten to
5089 <literal>e</literal>. You can also disable assertions using the
5090 <option>-fignore-asserts</option>
5091 option<indexterm><primary><option>-fignore-asserts</option></primary>
5092 </indexterm>.</para>
5095 Assertion failures can be caught, see the documentation for the
5096 <literal>Control.Exception</literal> library for the details.
5102 <!-- =============================== PRAGMAS =========================== -->
5104 <sect1 id="pragmas">
5105 <title>Pragmas</title>
5107 <indexterm><primary>pragma</primary></indexterm>
5109 <para>GHC supports several pragmas, or instructions to the
5110 compiler placed in the source code. Pragmas don't normally affect
5111 the meaning of the program, but they might affect the efficiency
5112 of the generated code.</para>
5114 <para>Pragmas all take the form
5116 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5118 where <replaceable>word</replaceable> indicates the type of
5119 pragma, and is followed optionally by information specific to that
5120 type of pragma. Case is ignored in
5121 <replaceable>word</replaceable>. The various values for
5122 <replaceable>word</replaceable> that GHC understands are described
5123 in the following sections; any pragma encountered with an
5124 unrecognised <replaceable>word</replaceable> is (silently)
5127 <sect2 id="deprecated-pragma">
5128 <title>DEPRECATED pragma</title>
5129 <indexterm><primary>DEPRECATED</primary>
5132 <para>The DEPRECATED pragma lets you specify that a particular
5133 function, class, or type, is deprecated. There are two
5138 <para>You can deprecate an entire module thus:</para>
5140 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5143 <para>When you compile any module that import
5144 <literal>Wibble</literal>, GHC will print the specified
5149 <para>You can deprecate a function, class, type, or data constructor, with the
5150 following top-level declaration:</para>
5152 {-# DEPRECATED f, C, T "Don't use these" #-}
5154 <para>When you compile any module that imports and uses any
5155 of the specified entities, GHC will print the specified
5157 <para> You can only depecate entities declared at top level in the module
5158 being compiled, and you can only use unqualified names in the list of
5159 entities being deprecated. A capitalised name, such as <literal>T</literal>
5160 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5161 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5162 both are in scope. If both are in scope, there is currently no way to deprecate
5163 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5166 Any use of the deprecated item, or of anything from a deprecated
5167 module, will be flagged with an appropriate message. However,
5168 deprecations are not reported for
5169 (a) uses of a deprecated function within its defining module, and
5170 (b) uses of a deprecated function in an export list.
5171 The latter reduces spurious complaints within a library
5172 in which one module gathers together and re-exports
5173 the exports of several others.
5175 <para>You can suppress the warnings with the flag
5176 <option>-fno-warn-deprecations</option>.</para>
5179 <sect2 id="include-pragma">
5180 <title>INCLUDE pragma</title>
5182 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5183 of C header files that should be <literal>#include</literal>'d into
5184 the C source code generated by the compiler for the current module (if
5185 compiling via C). For example:</para>
5188 {-# INCLUDE "foo.h" #-}
5189 {-# INCLUDE <stdio.h> #-}</programlisting>
5191 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5192 your source file with any <literal>OPTIONS_GHC</literal>
5195 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5196 to the <option>-#include</option> option (<xref
5197 linkend="options-C-compiler" />), because the
5198 <literal>INCLUDE</literal> pragma is understood by other
5199 compilers. Yet another alternative is to add the include file to each
5200 <literal>foreign import</literal> declaration in your code, but we
5201 don't recommend using this approach with GHC.</para>
5204 <sect2 id="inline-noinline-pragma">
5205 <title>INLINE and NOINLINE pragmas</title>
5207 <para>These pragmas control the inlining of function
5210 <sect3 id="inline-pragma">
5211 <title>INLINE pragma</title>
5212 <indexterm><primary>INLINE</primary></indexterm>
5214 <para>GHC (with <option>-O</option>, as always) tries to
5215 inline (or “unfold”) functions/values that are
5216 “small enough,” thus avoiding the call overhead
5217 and possibly exposing other more-wonderful optimisations.
5218 Normally, if GHC decides a function is “too
5219 expensive” to inline, it will not do so, nor will it
5220 export that unfolding for other modules to use.</para>
5222 <para>The sledgehammer you can bring to bear is the
5223 <literal>INLINE</literal><indexterm><primary>INLINE
5224 pragma</primary></indexterm> pragma, used thusly:</para>
5227 key_function :: Int -> String -> (Bool, Double)
5229 #ifdef __GLASGOW_HASKELL__
5230 {-# INLINE key_function #-}
5234 <para>(You don't need to do the C pre-processor carry-on
5235 unless you're going to stick the code through HBC—it
5236 doesn't like <literal>INLINE</literal> pragmas.)</para>
5238 <para>The major effect of an <literal>INLINE</literal> pragma
5239 is to declare a function's “cost” to be very low.
5240 The normal unfolding machinery will then be very keen to
5243 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5244 function can be put anywhere its type signature could be
5247 <para><literal>INLINE</literal> pragmas are a particularly
5249 <literal>then</literal>/<literal>return</literal> (or
5250 <literal>bind</literal>/<literal>unit</literal>) functions in
5251 a monad. For example, in GHC's own
5252 <literal>UniqueSupply</literal> monad code, we have:</para>
5255 #ifdef __GLASGOW_HASKELL__
5256 {-# INLINE thenUs #-}
5257 {-# INLINE returnUs #-}
5261 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5262 linkend="noinline-pragma"/>).</para>
5265 <sect3 id="noinline-pragma">
5266 <title>NOINLINE pragma</title>
5268 <indexterm><primary>NOINLINE</primary></indexterm>
5269 <indexterm><primary>NOTINLINE</primary></indexterm>
5271 <para>The <literal>NOINLINE</literal> pragma does exactly what
5272 you'd expect: it stops the named function from being inlined
5273 by the compiler. You shouldn't ever need to do this, unless
5274 you're very cautious about code size.</para>
5276 <para><literal>NOTINLINE</literal> is a synonym for
5277 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5278 specified by Haskell 98 as the standard way to disable
5279 inlining, so it should be used if you want your code to be
5283 <sect3 id="phase-control">
5284 <title>Phase control</title>
5286 <para> Sometimes you want to control exactly when in GHC's
5287 pipeline the INLINE pragma is switched on. Inlining happens
5288 only during runs of the <emphasis>simplifier</emphasis>. Each
5289 run of the simplifier has a different <emphasis>phase
5290 number</emphasis>; the phase number decreases towards zero.
5291 If you use <option>-dverbose-core2core</option> you'll see the
5292 sequence of phase numbers for successive runs of the
5293 simplifier. In an INLINE pragma you can optionally specify a
5297 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5298 <literal>f</literal>
5299 until phase <literal>k</literal>, but from phase
5300 <literal>k</literal> onwards be very keen to inline it.
5303 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5304 <literal>f</literal>
5305 until phase <literal>k</literal>, but from phase
5306 <literal>k</literal> onwards do not inline it.
5309 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5310 <literal>f</literal>
5311 until phase <literal>k</literal>, but from phase
5312 <literal>k</literal> onwards be willing to inline it (as if
5313 there was no pragma).
5316 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5317 <literal>f</literal>
5318 until phase <literal>k</literal>, but from phase
5319 <literal>k</literal> onwards do not inline it.
5322 The same information is summarised here:
5324 -- Before phase 2 Phase 2 and later
5325 {-# INLINE [2] f #-} -- No Yes
5326 {-# INLINE [~2] f #-} -- Yes No
5327 {-# NOINLINE [2] f #-} -- No Maybe
5328 {-# NOINLINE [~2] f #-} -- Maybe No
5330 {-# INLINE f #-} -- Yes Yes
5331 {-# NOINLINE f #-} -- No No
5333 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5334 function body is small, or it is applied to interesting-looking arguments etc).
5335 Another way to understand the semantics is this:
5337 <listitem><para>For both INLINE and NOINLINE, the phase number says
5338 when inlining is allowed at all.</para></listitem>
5339 <listitem><para>The INLINE pragma has the additional effect of making the
5340 function body look small, so that when inlining is allowed it is very likely to
5345 <para>The same phase-numbering control is available for RULES
5346 (<xref linkend="rewrite-rules"/>).</para>
5350 <sect2 id="language-pragma">
5351 <title>LANGUAGE pragma</title>
5353 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5354 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5356 <para>This allows language extensions to be enabled in a portable way.
5357 It is the intention that all Haskell compilers support the
5358 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5359 all extensions are supported by all compilers, of
5360 course. The <literal>LANGUAGE</literal> pragma should be used instead
5361 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5363 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5365 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5367 <para>Any extension from the <literal>Extension</literal> type defined in
5369 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>
5373 <sect2 id="line-pragma">
5374 <title>LINE pragma</title>
5376 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5377 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5378 <para>This pragma is similar to C's <literal>#line</literal>
5379 pragma, and is mainly for use in automatically generated Haskell
5380 code. It lets you specify the line number and filename of the
5381 original code; for example</para>
5383 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5385 <para>if you'd generated the current file from something called
5386 <filename>Foo.vhs</filename> and this line corresponds to line
5387 42 in the original. GHC will adjust its error messages to refer
5388 to the line/file named in the <literal>LINE</literal>
5392 <sect2 id="options-pragma">
5393 <title>OPTIONS_GHC pragma</title>
5394 <indexterm><primary>OPTIONS_GHC</primary>
5396 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5399 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5400 additional options that are given to the compiler when compiling
5401 this source file. See <xref linkend="source-file-options"/> for
5404 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5405 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5409 <title>RULES pragma</title>
5411 <para>The RULES pragma lets you specify rewrite rules. It is
5412 described in <xref linkend="rewrite-rules"/>.</para>
5415 <sect2 id="specialize-pragma">
5416 <title>SPECIALIZE pragma</title>
5418 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5419 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5420 <indexterm><primary>overloading, death to</primary></indexterm>
5422 <para>(UK spelling also accepted.) For key overloaded
5423 functions, you can create extra versions (NB: more code space)
5424 specialised to particular types. Thus, if you have an
5425 overloaded function:</para>
5428 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5431 <para>If it is heavily used on lists with
5432 <literal>Widget</literal> keys, you could specialise it as
5436 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5439 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5440 be put anywhere its type signature could be put.</para>
5442 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5443 (a) a specialised version of the function and (b) a rewrite rule
5444 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5445 un-specialised function into a call to the specialised one.</para>
5447 <para>The type in a SPECIALIZE pragma can be any type that is less
5448 polymorphic than the type of the original function. In concrete terms,
5449 if the original function is <literal>f</literal> then the pragma
5451 {-# SPECIALIZE f :: <type> #-}
5453 is valid if and only if the defintion
5455 f_spec :: <type>
5458 is valid. Here are some examples (where we only give the type signature
5459 for the original function, not its code):
5461 f :: Eq a => a -> b -> b
5462 {-# SPECIALISE f :: Int -> b -> b #-}
5464 g :: (Eq a, Ix b) => a -> b -> b
5465 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5467 h :: Eq a => a -> a -> a
5468 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5470 The last of these examples will generate a
5471 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5472 well. If you use this kind of specialisation, let us know how well it works.
5475 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5476 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5477 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5478 The <literal>INLINE</literal> pragma affects the specialised verison of the
5479 function (only), and applies even if the function is recursive. The motivating
5482 -- A GADT for arrays with type-indexed representation
5484 ArrInt :: !Int -> ByteArray# -> Arr Int
5485 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5487 (!:) :: Arr e -> Int -> e
5488 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5489 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5490 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5491 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5493 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5494 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5495 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5496 the specialised function will be inlined. It has two calls to
5497 <literal>(!:)</literal>,
5498 both at type <literal>Int</literal>. Both these calls fire the first
5499 specialisation, whose body is also inlined. The result is a type-based
5500 unrolling of the indexing function.</para>
5501 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5502 on an ordinarily-recursive function.</para>
5504 <para>Note: In earlier versions of GHC, it was possible to provide your own
5505 specialised function for a given type:
5508 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5511 This feature has been removed, as it is now subsumed by the
5512 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5516 <sect2 id="specialize-instance-pragma">
5517 <title>SPECIALIZE instance pragma
5521 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5522 <indexterm><primary>overloading, death to</primary></indexterm>
5523 Same idea, except for instance declarations. For example:
5526 instance (Eq a) => Eq (Foo a) where {
5527 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5531 The pragma must occur inside the <literal>where</literal> part
5532 of the instance declaration.
5535 Compatible with HBC, by the way, except perhaps in the placement
5541 <sect2 id="unpack-pragma">
5542 <title>UNPACK pragma</title>
5544 <indexterm><primary>UNPACK</primary></indexterm>
5546 <para>The <literal>UNPACK</literal> indicates to the compiler
5547 that it should unpack the contents of a constructor field into
5548 the constructor itself, removing a level of indirection. For
5552 data T = T {-# UNPACK #-} !Float
5553 {-# UNPACK #-} !Float
5556 <para>will create a constructor <literal>T</literal> containing
5557 two unboxed floats. This may not always be an optimisation: if
5558 the <function>T</function> constructor is scrutinised and the
5559 floats passed to a non-strict function for example, they will
5560 have to be reboxed (this is done automatically by the
5563 <para>Unpacking constructor fields should only be used in
5564 conjunction with <option>-O</option>, in order to expose
5565 unfoldings to the compiler so the reboxing can be removed as
5566 often as possible. For example:</para>
5570 f (T f1 f2) = f1 + f2
5573 <para>The compiler will avoid reboxing <function>f1</function>
5574 and <function>f2</function> by inlining <function>+</function>
5575 on floats, but only when <option>-O</option> is on.</para>
5577 <para>Any single-constructor data is eligible for unpacking; for
5581 data T = T {-# UNPACK #-} !(Int,Int)
5584 <para>will store the two <literal>Int</literal>s directly in the
5585 <function>T</function> constructor, by flattening the pair.
5586 Multi-level unpacking is also supported:</para>
5589 data T = T {-# UNPACK #-} !S
5590 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5593 <para>will store two unboxed <literal>Int#</literal>s
5594 directly in the <function>T</function> constructor. The
5595 unpacker can see through newtypes, too.</para>
5597 <para>If a field cannot be unpacked, you will not get a warning,
5598 so it might be an idea to check the generated code with
5599 <option>-ddump-simpl</option>.</para>
5601 <para>See also the <option>-funbox-strict-fields</option> flag,
5602 which essentially has the effect of adding
5603 <literal>{-# UNPACK #-}</literal> to every strict
5604 constructor field.</para>
5609 <!-- ======================= REWRITE RULES ======================== -->
5611 <sect1 id="rewrite-rules">
5612 <title>Rewrite rules
5614 <indexterm><primary>RULES pragma</primary></indexterm>
5615 <indexterm><primary>pragma, RULES</primary></indexterm>
5616 <indexterm><primary>rewrite rules</primary></indexterm></title>
5619 The programmer can specify rewrite rules as part of the source program
5620 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5621 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5622 and (b) the <option>-frules-off</option> flag
5623 (<xref linkend="options-f"/>) is not specified, and (c) the
5624 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5633 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5640 <title>Syntax</title>
5643 From a syntactic point of view:
5649 There may be zero or more rules in a <literal>RULES</literal> pragma.
5656 Each rule has a name, enclosed in double quotes. The name itself has
5657 no significance at all. It is only used when reporting how many times the rule fired.
5663 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5664 immediately after the name of the rule. Thus:
5667 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5670 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5671 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5680 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5681 is set, so you must lay out your rules starting in the same column as the
5682 enclosing definitions.
5689 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5690 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5691 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5692 by spaces, just like in a type <literal>forall</literal>.
5698 A pattern variable may optionally have a type signature.
5699 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5700 For example, here is the <literal>foldr/build</literal> rule:
5703 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5704 foldr k z (build g) = g k z
5707 Since <function>g</function> has a polymorphic type, it must have a type signature.
5714 The left hand side of a rule must consist of a top-level variable applied
5715 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5718 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5719 "wrong2" forall f. f True = True
5722 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5729 A rule does not need to be in the same module as (any of) the
5730 variables it mentions, though of course they need to be in scope.
5736 Rules are automatically exported from a module, just as instance declarations are.
5747 <title>Semantics</title>
5750 From a semantic point of view:
5756 Rules are only applied if you use the <option>-O</option> flag.
5762 Rules are regarded as left-to-right rewrite rules.
5763 When GHC finds an expression that is a substitution instance of the LHS
5764 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5765 By "a substitution instance" we mean that the LHS can be made equal to the
5766 expression by substituting for the pattern variables.
5773 The LHS and RHS of a rule are typechecked, and must have the
5781 GHC makes absolutely no attempt to verify that the LHS and RHS
5782 of a rule have the same meaning. That is undecidable in general, and
5783 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5790 GHC makes no attempt to make sure that the rules are confluent or
5791 terminating. For example:
5794 "loop" forall x,y. f x y = f y x
5797 This rule will cause the compiler to go into an infinite loop.
5804 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5810 GHC currently uses a very simple, syntactic, matching algorithm
5811 for matching a rule LHS with an expression. It seeks a substitution
5812 which makes the LHS and expression syntactically equal modulo alpha
5813 conversion. The pattern (rule), but not the expression, is eta-expanded if
5814 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5815 But not beta conversion (that's called higher-order matching).
5819 Matching is carried out on GHC's intermediate language, which includes
5820 type abstractions and applications. So a rule only matches if the
5821 types match too. See <xref linkend="rule-spec"/> below.
5827 GHC keeps trying to apply the rules as it optimises the program.
5828 For example, consider:
5837 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5838 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5839 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5840 not be substituted, and the rule would not fire.
5847 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5848 that appears on the LHS of a rule</emphasis>, because once you have substituted
5849 for something you can't match against it (given the simple minded
5850 matching). So if you write the rule
5853 "map/map" forall f,g. map f . map g = map (f.g)
5856 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5857 It will only match something written with explicit use of ".".
5858 Well, not quite. It <emphasis>will</emphasis> match the expression
5864 where <function>wibble</function> is defined:
5867 wibble f g = map f . map g
5870 because <function>wibble</function> will be inlined (it's small).
5872 Later on in compilation, GHC starts inlining even things on the
5873 LHS of rules, but still leaves the rules enabled. This inlining
5874 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5881 All rules are implicitly exported from the module, and are therefore
5882 in force in any module that imports the module that defined the rule, directly
5883 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5884 in force when compiling A.) The situation is very similar to that for instance
5896 <title>List fusion</title>
5899 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5900 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5901 intermediate list should be eliminated entirely.
5905 The following are good producers:
5917 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5923 Explicit lists (e.g. <literal>[True, False]</literal>)
5929 The cons constructor (e.g <literal>3:4:[]</literal>)
5935 <function>++</function>
5941 <function>map</function>
5947 <function>take</function>, <function>filter</function>
5953 <function>iterate</function>, <function>repeat</function>
5959 <function>zip</function>, <function>zipWith</function>
5968 The following are good consumers:
5980 <function>array</function> (on its second argument)
5986 <function>++</function> (on its first argument)
5992 <function>foldr</function>
5998 <function>map</function>
6004 <function>take</function>, <function>filter</function>
6010 <function>concat</function>
6016 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6022 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6023 will fuse with one but not the other)
6029 <function>partition</function>
6035 <function>head</function>
6041 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6047 <function>sequence_</function>
6053 <function>msum</function>
6059 <function>sortBy</function>
6068 So, for example, the following should generate no intermediate lists:
6071 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6077 This list could readily be extended; if there are Prelude functions that you use
6078 a lot which are not included, please tell us.
6082 If you want to write your own good consumers or producers, look at the
6083 Prelude definitions of the above functions to see how to do so.
6088 <sect2 id="rule-spec">
6089 <title>Specialisation
6093 Rewrite rules can be used to get the same effect as a feature
6094 present in earlier versions of GHC.
6095 For example, suppose that:
6098 genericLookup :: Ord a => Table a b -> a -> b
6099 intLookup :: Table Int b -> Int -> b
6102 where <function>intLookup</function> is an implementation of
6103 <function>genericLookup</function> that works very fast for
6104 keys of type <literal>Int</literal>. You might wish
6105 to tell GHC to use <function>intLookup</function> instead of
6106 <function>genericLookup</function> whenever the latter was called with
6107 type <literal>Table Int b -> Int -> b</literal>.
6108 It used to be possible to write
6111 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6114 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6117 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6120 This slightly odd-looking rule instructs GHC to replace
6121 <function>genericLookup</function> by <function>intLookup</function>
6122 <emphasis>whenever the types match</emphasis>.
6123 What is more, this rule does not need to be in the same
6124 file as <function>genericLookup</function>, unlike the
6125 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6126 have an original definition available to specialise).
6129 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6130 <function>intLookup</function> really behaves as a specialised version
6131 of <function>genericLookup</function>!!!</para>
6133 <para>An example in which using <literal>RULES</literal> for
6134 specialisation will Win Big:
6137 toDouble :: Real a => a -> Double
6138 toDouble = fromRational . toRational
6140 {-# RULES "toDouble/Int" toDouble = i2d #-}
6141 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6144 The <function>i2d</function> function is virtually one machine
6145 instruction; the default conversion—via an intermediate
6146 <literal>Rational</literal>—is obscenely expensive by
6153 <title>Controlling what's going on</title>
6161 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6167 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6168 If you add <option>-dppr-debug</option> you get a more detailed listing.
6174 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6177 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6178 {-# INLINE build #-}
6182 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6183 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6184 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6185 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6192 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6193 see how to write rules that will do fusion and yet give an efficient
6194 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6204 <sect2 id="core-pragma">
6205 <title>CORE pragma</title>
6207 <indexterm><primary>CORE pragma</primary></indexterm>
6208 <indexterm><primary>pragma, CORE</primary></indexterm>
6209 <indexterm><primary>core, annotation</primary></indexterm>
6212 The external core format supports <quote>Note</quote> annotations;
6213 the <literal>CORE</literal> pragma gives a way to specify what these
6214 should be in your Haskell source code. Syntactically, core
6215 annotations are attached to expressions and take a Haskell string
6216 literal as an argument. The following function definition shows an
6220 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6223 Semantically, this is equivalent to:
6231 However, when external for is generated (via
6232 <option>-fext-core</option>), there will be Notes attached to the
6233 expressions <function>show</function> and <varname>x</varname>.
6234 The core function declaration for <function>f</function> is:
6238 f :: %forall a . GHCziShow.ZCTShow a ->
6239 a -> GHCziBase.ZMZN GHCziBase.Char =
6240 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6242 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6244 (tpl1::GHCziBase.Int ->
6246 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6248 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6249 (tpl3::GHCziBase.ZMZN a ->
6250 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6258 Here, we can see that the function <function>show</function> (which
6259 has been expanded out to a case expression over the Show dictionary)
6260 has a <literal>%note</literal> attached to it, as does the
6261 expression <varname>eta</varname> (which used to be called
6262 <varname>x</varname>).
6269 <sect1 id="special-ids">
6270 <title>Special built-in functions</title>
6271 <para>GHC has a few built-in funcions with special behaviour,
6272 described in this section. All are exported by
6273 <literal>GHC.Exts</literal>.</para>
6275 <sect2> <title>The <literal>seq</literal> function </title>
6277 The function <literal>seq</literal> is as described in the Haskell98 Report.
6281 It evaluates its first argument to head normal form, and then returns its
6282 second argument as the result. The reason that it is documented here is
6283 that, despite <literal>seq</literal>'s polymorphism, its
6284 second argument can have an unboxed type, or
6285 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6286 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6287 to be instantiated to an unboxed type, which is not usually allowed.
6291 <sect2> <title>The <literal>inline</literal> function </title>
6293 The <literal>inline</literal> function is somewhat experimental.
6297 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6298 is inlined, regardless of its size. More precisely, the call
6299 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6301 This allows the programmer to control inlining from
6302 a particular <emphasis>call site</emphasis>
6303 rather than the <emphasis>definition site</emphasis> of the function
6304 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6307 This inlining occurs regardless of the argument to the call
6308 or the size of <literal>f</literal>'s definition; it is unconditional.
6309 The main caveat is that <literal>f</literal>'s definition must be
6310 visible to the compiler. That is, <literal>f</literal> must be
6311 let-bound in the current scope.
6312 If no inlining takes place, the <literal>inline</literal> function
6313 expands to the identity function in Phase zero; so its use imposes
6316 <para> If the function is defined in another
6317 module, GHC only exposes its inlining in the interface file if the
6318 function is sufficiently small that it <emphasis>might</emphasis> be
6319 inlined by the automatic mechanism. There is currently no way to tell
6320 GHC to expose arbitrarily-large functions in the interface file. (This
6321 shortcoming is something that could be fixed, with some kind of pragma.)
6325 <sect2> <title>The <literal>lazy</literal> function </title>
6327 The <literal>lazy</literal> function restrains strictness analysis a little:
6331 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6332 but <literal>lazy</literal> has a magical property so far as strictness
6333 analysis is concerned: it is lazy in its first argument,
6334 even though its semantics is strict. After strictness analysis has run,
6335 calls to <literal>lazy</literal> are inlined to be the identity function.
6338 This behaviour is occasionally useful when controlling evaluation order.
6339 Notably, <literal>lazy</literal> is used in the library definition of
6340 <literal>Control.Parallel.par</literal>:
6343 par x y = case (par# x) of { _ -> lazy y }
6345 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6346 look strict in <literal>y</literal> which would defeat the whole
6347 purpose of <literal>par</literal>.
6350 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6356 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6358 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6359 typechecker entirely. It has type
6361 unsafeCoerce# :: a -> b
6363 That is, it allows you to coerce any type into any other type. If you use this
6364 function, you had better get it right, otherwise segmentation faults await.
6365 It is generally used when you want to write a program that you know is
6366 well-typed, but where Haskell's type system is not expressive enough to prove
6367 that it is well typed.
6370 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6371 although extremely bad things will happen if you coerce a boxed type
6380 <sect1 id="generic-classes">
6381 <title>Generic classes</title>
6384 The ideas behind this extension are described in detail in "Derivable type classes",
6385 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6386 An example will give the idea:
6394 fromBin :: [Int] -> (a, [Int])
6396 toBin {| Unit |} Unit = []
6397 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6398 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6399 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6401 fromBin {| Unit |} bs = (Unit, bs)
6402 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6403 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6404 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6405 (y,bs'') = fromBin bs'
6408 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6409 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6410 which are defined thus in the library module <literal>Generics</literal>:
6414 data a :+: b = Inl a | Inr b
6415 data a :*: b = a :*: b
6418 Now you can make a data type into an instance of Bin like this:
6420 instance (Bin a, Bin b) => Bin (a,b)
6421 instance Bin a => Bin [a]
6423 That is, just leave off the "where" clause. Of course, you can put in the
6424 where clause and over-ride whichever methods you please.
6428 <title> Using generics </title>
6429 <para>To use generics you need to</para>
6432 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6433 <option>-fgenerics</option> (to generate extra per-data-type code),
6434 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6438 <para>Import the module <literal>Generics</literal> from the
6439 <literal>lang</literal> package. This import brings into
6440 scope the data types <literal>Unit</literal>,
6441 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6442 don't need this import if you don't mention these types
6443 explicitly; for example, if you are simply giving instance
6444 declarations.)</para>
6449 <sect2> <title> Changes wrt the paper </title>
6451 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6452 can be written infix (indeed, you can now use
6453 any operator starting in a colon as an infix type constructor). Also note that
6454 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6455 Finally, note that the syntax of the type patterns in the class declaration
6456 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6457 alone would ambiguous when they appear on right hand sides (an extension we
6458 anticipate wanting).
6462 <sect2> <title>Terminology and restrictions</title>
6464 Terminology. A "generic default method" in a class declaration
6465 is one that is defined using type patterns as above.
6466 A "polymorphic default method" is a default method defined as in Haskell 98.
6467 A "generic class declaration" is a class declaration with at least one
6468 generic default method.
6476 Alas, we do not yet implement the stuff about constructor names and
6483 A generic class can have only one parameter; you can't have a generic
6484 multi-parameter class.
6490 A default method must be defined entirely using type patterns, or entirely
6491 without. So this is illegal:
6494 op :: a -> (a, Bool)
6495 op {| Unit |} Unit = (Unit, True)
6498 However it is perfectly OK for some methods of a generic class to have
6499 generic default methods and others to have polymorphic default methods.
6505 The type variable(s) in the type pattern for a generic method declaration
6506 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:
6510 op {| p :*: q |} (x :*: y) = op (x :: p)
6518 The type patterns in a generic default method must take one of the forms:
6524 where "a" and "b" are type variables. Furthermore, all the type patterns for
6525 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6526 must use the same type variables. So this is illegal:
6530 op {| a :+: b |} (Inl x) = True
6531 op {| p :+: q |} (Inr y) = False
6533 The type patterns must be identical, even in equations for different methods of the class.
6534 So this too is illegal:
6538 op1 {| a :*: b |} (x :*: y) = True
6541 op2 {| p :*: q |} (x :*: y) = False
6543 (The reason for this restriction is that we gather all the equations for a particular type consructor
6544 into a single generic instance declaration.)
6550 A generic method declaration must give a case for each of the three type constructors.
6556 The type for a generic method can be built only from:
6558 <listitem> <para> Function arrows </para> </listitem>
6559 <listitem> <para> Type variables </para> </listitem>
6560 <listitem> <para> Tuples </para> </listitem>
6561 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6563 Here are some example type signatures for generic methods:
6566 op2 :: Bool -> (a,Bool)
6567 op3 :: [Int] -> a -> a
6570 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6574 This restriction is an implementation restriction: we just havn't got around to
6575 implementing the necessary bidirectional maps over arbitrary type constructors.
6576 It would be relatively easy to add specific type constructors, such as Maybe and list,
6577 to the ones that are allowed.</para>
6582 In an instance declaration for a generic class, the idea is that the compiler
6583 will fill in the methods for you, based on the generic templates. However it can only
6588 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6593 No constructor of the instance type has unboxed fields.
6597 (Of course, these things can only arise if you are already using GHC extensions.)
6598 However, you can still give an instance declarations for types which break these rules,
6599 provided you give explicit code to override any generic default methods.
6607 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6608 what the compiler does with generic declarations.
6613 <sect2> <title> Another example </title>
6615 Just to finish with, here's another example I rather like:
6619 nCons {| Unit |} _ = 1
6620 nCons {| a :*: b |} _ = 1
6621 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6624 tag {| Unit |} _ = 1
6625 tag {| a :*: b |} _ = 1
6626 tag {| a :+: b |} (Inl x) = tag x
6627 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6633 <sect1 id="monomorphism">
6634 <title>Control over monomorphism</title>
6636 <para>GHC supports two flags that control the way in which generalisation is
6637 carried out at let and where bindings.
6641 <title>Switching off the dreaded Monomorphism Restriction</title>
6642 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6644 <para>Haskell's monomorphism restriction (see
6645 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6647 of the Haskell Report)
6648 can be completely switched off by
6649 <option>-fno-monomorphism-restriction</option>.
6654 <title>Monomorphic pattern bindings</title>
6655 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6656 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6658 <para> As an experimental change, we are exploring the possibility of
6659 making pattern bindings monomorphic; that is, not generalised at all.
6660 A pattern binding is a binding whose LHS has no function arguments,
6661 and is not a simple variable. For example:
6663 f x = x -- Not a pattern binding
6664 f = \x -> x -- Not a pattern binding
6665 f :: Int -> Int = \x -> x -- Not a pattern binding
6667 (g,h) = e -- A pattern binding
6668 (f) = e -- A pattern binding
6669 [x] = e -- A pattern binding
6671 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6672 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6681 ;;; Local Variables: ***
6683 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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