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>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>The flag <option>-fglasgow-exts</option>:
56 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
57 simultaneously enables the following extensions:
58 <option>-XForeignFunctionInterface</option>,
59 <option>-XImplicitParams</option>,
60 <option>-XScopedTypeVariables</option>,
61 <option>-XGADTs</option>,
62 <option>-XTypeFamilies</option>.
63 Enabling these options is the <emphasis>only</emphasis>
64 effect of <options>-fglasgow-exts</options>
65 We are trying to move away from this portmanteau flag,
66 and towards enabling features individually.</para>
70 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
71 <sect1 id="primitives">
72 <title>Unboxed types and primitive operations</title>
74 <para>GHC is built on a raft of primitive data types and operations;
75 "primitive" in the sense that they cannot be defined in Haskell itself.
76 While you really can use this stuff to write fast code,
77 we generally find it a lot less painful, and more satisfying in the
78 long run, to use higher-level language features and libraries. With
79 any luck, the code you write will be optimised to the efficient
80 unboxed version in any case. And if it isn't, we'd like to know
83 <para>All these primitive data types and operations are exported by the
84 library <literal>GHC.Prim</literal>, for which there is
85 <ulink url="../libraries/base/GHC.Prim.html">detailed online documentation</ulink>.
86 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
89 If you want to mention any of the primitive data types or operations in your
90 program, you must first import <literal>GHC.Prim</literal> to bring them
91 into scope. Many of them have names ending in "#", and to mention such
92 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
95 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
96 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
97 we briefly summarise here. </para>
99 <sect2 id="glasgow-unboxed">
104 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
107 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
108 that values of that type are represented by a pointer to a heap
109 object. The representation of a Haskell <literal>Int</literal>, for
110 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
111 type, however, is represented by the value itself, no pointers or heap
112 allocation are involved.
116 Unboxed types correspond to the “raw machine” types you
117 would use in C: <literal>Int#</literal> (long int),
118 <literal>Double#</literal> (double), <literal>Addr#</literal>
119 (void *), etc. The <emphasis>primitive operations</emphasis>
120 (PrimOps) on these types are what you might expect; e.g.,
121 <literal>(+#)</literal> is addition on
122 <literal>Int#</literal>s, and is the machine-addition that we all
123 know and love—usually one instruction.
127 Primitive (unboxed) types cannot be defined in Haskell, and are
128 therefore built into the language and compiler. Primitive types are
129 always unlifted; that is, a value of a primitive type cannot be
130 bottom. We use the convention (but it is only a convention)
131 that primitive types, values, and
132 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
133 For some primitive types we have special syntax for literals, also
134 described in the <link linkend="magic-hash">same section</link>.
138 Primitive values are often represented by a simple bit-pattern, such
139 as <literal>Int#</literal>, <literal>Float#</literal>,
140 <literal>Double#</literal>. But this is not necessarily the case:
141 a primitive value might be represented by a pointer to a
142 heap-allocated object. Examples include
143 <literal>Array#</literal>, the type of primitive arrays. A
144 primitive array is heap-allocated because it is too big a value to fit
145 in a register, and would be too expensive to copy around; in a sense,
146 it is accidental that it is represented by a pointer. If a pointer
147 represents a primitive value, then it really does point to that value:
148 no unevaluated thunks, no indirections…nothing can be at the
149 other end of the pointer than the primitive value.
150 A numerically-intensive program using unboxed types can
151 go a <emphasis>lot</emphasis> faster than its “standard”
152 counterpart—we saw a threefold speedup on one example.
156 There are some restrictions on the use of primitive types:
158 <listitem><para>The main restriction
159 is that you can't pass a primitive value to a polymorphic
160 function or store one in a polymorphic data type. This rules out
161 things like <literal>[Int#]</literal> (i.e. lists of primitive
162 integers). The reason for this restriction is that polymorphic
163 arguments and constructor fields are assumed to be pointers: if an
164 unboxed integer is stored in one of these, the garbage collector would
165 attempt to follow it, leading to unpredictable space leaks. Or a
166 <function>seq</function> operation on the polymorphic component may
167 attempt to dereference the pointer, with disastrous results. Even
168 worse, the unboxed value might be larger than a pointer
169 (<literal>Double#</literal> for instance).
172 <listitem><para> You cannot define a newtype whose representation type
173 (the argument type of the data constructor) is an unboxed type. Thus,
179 <listitem><para> You cannot bind a variable with an unboxed type
180 in a <emphasis>top-level</emphasis> binding.
182 <listitem><para> You cannot bind a variable with an unboxed type
183 in a <emphasis>recursive</emphasis> binding.
185 <listitem><para> You may bind unboxed variables in a (non-recursive,
186 non-top-level) pattern binding, but any such variable causes the entire
188 to become strict. For example:
190 data Foo = Foo Int Int#
192 f x = let (Foo a b, w) = ..rhs.. in ..body..
194 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
196 is strict, and the program behaves as if you had written
198 data Foo = Foo Int Int#
200 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
209 <sect2 id="unboxed-tuples">
210 <title>Unboxed Tuples
214 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
215 they're available by default with <option>-fglasgow-exts</option>. An
216 unboxed tuple looks like this:
228 where <literal>e_1..e_n</literal> are expressions of any
229 type (primitive or non-primitive). The type of an unboxed tuple looks
234 Unboxed tuples are used for functions that need to return multiple
235 values, but they avoid the heap allocation normally associated with
236 using fully-fledged tuples. When an unboxed tuple is returned, the
237 components are put directly into registers or on the stack; the
238 unboxed tuple itself does not have a composite representation. Many
239 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
241 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
242 tuples to avoid unnecessary allocation during sequences of operations.
246 There are some pretty stringent restrictions on the use of unboxed tuples:
251 Values of unboxed tuple types are subject to the same restrictions as
252 other unboxed types; i.e. they may not be stored in polymorphic data
253 structures or passed to polymorphic functions.
260 No variable can have an unboxed tuple type, nor may a constructor or function
261 argument have an unboxed tuple type. The following are all illegal:
265 data Foo = Foo (# Int, Int #)
267 f :: (# Int, Int #) -> (# Int, Int #)
270 g :: (# Int, Int #) -> Int
273 h x = let y = (# x,x #) in ...
280 The typical use of unboxed tuples is simply to return multiple values,
281 binding those multiple results with a <literal>case</literal> expression, thus:
283 f x y = (# x+1, y-1 #)
284 g x = case f x x of { (# a, b #) -> a + b }
286 You can have an unboxed tuple in a pattern binding, thus
288 f x = let (# p,q #) = h x in ..body..
290 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
291 the resulting binding is lazy like any other Haskell pattern binding. The
292 above example desugars like this:
294 f x = let t = case h x o f{ (# p,q #) -> (p,q)
299 Indeed, the bindings can even be recursive.
306 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
308 <sect1 id="syntax-extns">
309 <title>Syntactic extensions</title>
311 <sect2 id="magic-hash">
312 <title>The magic hash</title>
313 <para>The language extension <option>-XMagicHash</option> allows "#" as a
314 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
315 a valid type constructor or data constructor.</para>
317 <para>The hash sign does not change sematics at all. We tend to use variable
318 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
319 but there is no requirement to do so; they are just plain ordinary variables.
320 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
321 For example, to bring <literal>Int#</literal> into scope you must
322 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
323 the <option>-XMagicHash</option> extension
324 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
325 that is now in scope.</para>
326 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
328 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
329 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
330 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
331 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
332 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
333 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
334 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
335 is a <literal>Word#</literal>. </para> </listitem>
336 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
337 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
342 <!-- ====================== HIERARCHICAL MODULES ======================= -->
345 <sect2 id="hierarchical-modules">
346 <title>Hierarchical Modules</title>
348 <para>GHC supports a small extension to the syntax of module
349 names: a module name is allowed to contain a dot
350 <literal>‘.’</literal>. This is also known as the
351 “hierarchical module namespace” extension, because
352 it extends the normally flat Haskell module namespace into a
353 more flexible hierarchy of modules.</para>
355 <para>This extension has very little impact on the language
356 itself; modules names are <emphasis>always</emphasis> fully
357 qualified, so you can just think of the fully qualified module
358 name as <quote>the module name</quote>. In particular, this
359 means that the full module name must be given after the
360 <literal>module</literal> keyword at the beginning of the
361 module; for example, the module <literal>A.B.C</literal> must
364 <programlisting>module A.B.C</programlisting>
367 <para>It is a common strategy to use the <literal>as</literal>
368 keyword to save some typing when using qualified names with
369 hierarchical modules. For example:</para>
372 import qualified Control.Monad.ST.Strict as ST
375 <para>For details on how GHC searches for source and interface
376 files in the presence of hierarchical modules, see <xref
377 linkend="search-path"/>.</para>
379 <para>GHC comes with a large collection of libraries arranged
380 hierarchically; see the accompanying <ulink
381 url="../libraries/index.html">library
382 documentation</ulink>. More libraries to install are available
384 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
387 <!-- ====================== PATTERN GUARDS ======================= -->
389 <sect2 id="pattern-guards">
390 <title>Pattern guards</title>
393 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
394 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.)
398 Suppose we have an abstract data type of finite maps, with a
402 lookup :: FiniteMap -> Int -> Maybe Int
405 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
406 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
410 clunky env var1 var2 | ok1 && ok2 = val1 + val2
411 | otherwise = var1 + var2
422 The auxiliary functions are
426 maybeToBool :: Maybe a -> Bool
427 maybeToBool (Just x) = True
428 maybeToBool Nothing = False
430 expectJust :: Maybe a -> a
431 expectJust (Just x) = x
432 expectJust Nothing = error "Unexpected Nothing"
436 What is <function>clunky</function> doing? The guard <literal>ok1 &&
437 ok2</literal> checks that both lookups succeed, using
438 <function>maybeToBool</function> to convert the <function>Maybe</function>
439 types to booleans. The (lazily evaluated) <function>expectJust</function>
440 calls extract the values from the results of the lookups, and binds the
441 returned values to <varname>val1</varname> and <varname>val2</varname>
442 respectively. If either lookup fails, then clunky takes the
443 <literal>otherwise</literal> case and returns the sum of its arguments.
447 This is certainly legal Haskell, but it is a tremendously verbose and
448 un-obvious way to achieve the desired effect. Arguably, a more direct way
449 to write clunky would be to use case expressions:
453 clunky env var1 var2 = case lookup env var1 of
455 Just val1 -> case lookup env var2 of
457 Just val2 -> val1 + val2
463 This is a bit shorter, but hardly better. Of course, we can rewrite any set
464 of pattern-matching, guarded equations as case expressions; that is
465 precisely what the compiler does when compiling equations! The reason that
466 Haskell provides guarded equations is because they allow us to write down
467 the cases we want to consider, one at a time, independently of each other.
468 This structure is hidden in the case version. Two of the right-hand sides
469 are really the same (<function>fail</function>), and the whole expression
470 tends to become more and more indented.
474 Here is how I would write clunky:
479 | Just val1 <- lookup env var1
480 , Just val2 <- lookup env var2
482 ...other equations for clunky...
486 The semantics should be clear enough. The qualifiers are matched in order.
487 For a <literal><-</literal> qualifier, which I call a pattern guard, the
488 right hand side is evaluated and matched against the pattern on the left.
489 If the match fails then the whole guard fails and the next equation is
490 tried. If it succeeds, then the appropriate binding takes place, and the
491 next qualifier is matched, in the augmented environment. Unlike list
492 comprehensions, however, the type of the expression to the right of the
493 <literal><-</literal> is the same as the type of the pattern to its
494 left. The bindings introduced by pattern guards scope over all the
495 remaining guard qualifiers, and over the right hand side of the equation.
499 Just as with list comprehensions, boolean expressions can be freely mixed
500 with among the pattern guards. For example:
511 Haskell's current guards therefore emerge as a special case, in which the
512 qualifier list has just one element, a boolean expression.
516 <!-- ===================== View patterns =================== -->
518 <sect2 id="view-patterns">
523 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
524 More information and examples of view patterns can be found on the
525 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
530 View patterns are somewhat like pattern guards that can be nested inside
531 of other patterns. They are a convenient way of pattern-matching
532 against values of abstract types. For example, in a programming language
533 implementation, we might represent the syntax of the types of the
542 view :: Type -> TypeView
544 -- additional operations for constructing Typ's ...
547 The representation of Typ is held abstract, permitting implementations
548 to use a fancy representation (e.g., hash-consing to manage sharing).
550 Without view patterns, using this signature a little inconvenient:
552 size :: Typ -> Integer
553 size t = case view t of
555 Arrow t1 t2 -> size t1 + size t2
558 It is necessary to iterate the case, rather than using an equational
559 function definition. And the situation is even worse when the matching
560 against <literal>t</literal> is buried deep inside another pattern.
564 View patterns permit calling the view function inside the pattern and
565 matching against the result:
567 size (view -> Unit) = 1
568 size (view -> Arrow t1 t2) = size t1 + size t2
571 That is, we add a new form of pattern, written
572 <replaceable>expression</replaceable> <literal>-></literal>
573 <replaceable>pattern</replaceable> that means "apply the expression to
574 whatever we're trying to match against, and then match the result of
575 that application against the pattern". The expression can be any Haskell
576 expression of function type, and view patterns can be used wherever
581 The semantics of a pattern <literal>(</literal>
582 <replaceable>exp</replaceable> <literal>-></literal>
583 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
589 <para>The variables bound by the view pattern are the variables bound by
590 <replaceable>pat</replaceable>.
594 Any variables in <replaceable>exp</replaceable> are bound occurrences,
595 but variables bound "to the left" in a pattern are in scope. This
596 feature permits, for example, one argument to a function to be used in
597 the view of another argument. For example, the function
598 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
599 written using view patterns as follows:
602 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
603 ...other equations for clunky...
608 More precisely, the scoping rules are:
612 In a single pattern, variables bound by patterns to the left of a view
613 pattern expression are in scope. For example:
615 example :: Maybe ((String -> Integer,Integer), String) -> Bool
616 example Just ((f,_), f -> 4) = True
619 Additionally, in function definitions, variables bound by matching earlier curried
620 arguments may be used in view pattern expressions in later arguments:
622 example :: (String -> Integer) -> String -> Bool
623 example f (f -> 4) = True
625 That is, the scoping is the same as it would be if the curried arguments
626 were collected into a tuple.
632 In mutually recursive bindings, such as <literal>let</literal>,
633 <literal>where</literal>, or the top level, view patterns in one
634 declaration may not mention variables bound by other declarations. That
635 is, each declaration must be self-contained. For example, the following
636 program is not allowed:
643 restriction in the future; the only cost is that type checking patterns
644 would get a little more complicated.)
654 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
655 <replaceable>T1</replaceable> <literal>-></literal>
656 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
657 a <replaceable>T2</replaceable>, then the whole view pattern matches a
658 <replaceable>T1</replaceable>.
661 <listitem><para> Matching: To the equations in Section 3.17.3 of the
662 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
663 Report</ulink>, add the following:
665 case v of { (e -> p) -> e1 ; _ -> e2 }
667 case (e v) of { p -> e1 ; _ -> e2 }
669 That is, to match a variable <replaceable>v</replaceable> against a pattern
670 <literal>(</literal> <replaceable>exp</replaceable>
671 <literal>-></literal> <replaceable>pat</replaceable>
672 <literal>)</literal>, evaluate <literal>(</literal>
673 <replaceable>exp</replaceable> <replaceable> v</replaceable>
674 <literal>)</literal> and match the result against
675 <replaceable>pat</replaceable>.
678 <listitem><para> Efficiency: When the same view function is applied in
679 multiple branches of a function definition or a case expression (e.g.,
680 in <literal>size</literal> above), GHC makes an attempt to collect these
681 applications into a single nested case expression, so that the view
682 function is only applied once. Pattern compilation in GHC follows the
683 matrix algorithm described in Chapter 4 of <ulink
684 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
685 Implementation of Functional Programming Languages</ulink>. When the
686 top rows of the first column of a matrix are all view patterns with the
687 "same" expression, these patterns are transformed into a single nested
688 case. This includes, for example, adjacent view patterns that line up
691 f ((view -> A, p1), p2) = e1
692 f ((view -> B, p3), p4) = e2
696 <para> The current notion of when two view pattern expressions are "the
697 same" is very restricted: it is not even full syntactic equality.
698 However, it does include variables, literals, applications, and tuples;
699 e.g., two instances of <literal>view ("hi", "there")</literal> will be
700 collected. However, the current implementation does not compare up to
701 alpha-equivalence, so two instances of <literal>(x, view x ->
702 y)</literal> will not be coalesced.
712 <!-- ===================== Recursive do-notation =================== -->
714 <sect2 id="mdo-notation">
715 <title>The recursive do-notation
718 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
719 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
720 by Levent Erkok, John Launchbury,
721 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
722 This paper is essential reading for anyone making non-trivial use of mdo-notation,
723 and we do not repeat it here.
726 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
727 that is, the variables bound in a do-expression are visible only in the textually following
728 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
729 group. It turns out that several applications can benefit from recursive bindings in
730 the do-notation, and this extension provides the necessary syntactic support.
733 Here is a simple (yet contrived) example:
736 import Control.Monad.Fix
738 justOnes = mdo xs <- Just (1:xs)
742 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
746 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
749 class Monad m => MonadFix m where
750 mfix :: (a -> m a) -> m a
753 The function <literal>mfix</literal>
754 dictates how the required recursion operation should be performed. For example,
755 <literal>justOnes</literal> desugars as follows:
757 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
759 For full details of the way in which mdo is typechecked and desugared, see
760 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
761 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
764 If recursive bindings are required for a monad,
765 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
766 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
767 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
768 for Haskell's internal state monad (strict and lazy, respectively).
771 Here are some important points in using the recursive-do notation:
774 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
775 than <literal>do</literal>).
779 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
780 <literal>-fglasgow-exts</literal>.
784 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
785 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
786 be distinct (Section 3.3 of the paper).
790 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
791 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
792 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
793 and improve termination (Section 3.2 of the paper).
799 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb/">http://www.cse.ogi.edu/PacSoft/projects/rmb/</ulink>
800 contains up to date information on recursive monadic bindings.
804 Historical note: The old implementation of the mdo-notation (and most
805 of the existing documents) used the name
806 <literal>MonadRec</literal> for the class and the corresponding library.
807 This name is not supported by GHC.
813 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
815 <sect2 id="parallel-list-comprehensions">
816 <title>Parallel List Comprehensions</title>
817 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
819 <indexterm><primary>parallel list comprehensions</primary>
822 <para>Parallel list comprehensions are a natural extension to list
823 comprehensions. List comprehensions can be thought of as a nice
824 syntax for writing maps and filters. Parallel comprehensions
825 extend this to include the zipWith family.</para>
827 <para>A parallel list comprehension has multiple independent
828 branches of qualifier lists, each separated by a `|' symbol. For
829 example, the following zips together two lists:</para>
832 [ (x, y) | x <- xs | y <- ys ]
835 <para>The behavior of parallel list comprehensions follows that of
836 zip, in that the resulting list will have the same length as the
837 shortest branch.</para>
839 <para>We can define parallel list comprehensions by translation to
840 regular comprehensions. Here's the basic idea:</para>
842 <para>Given a parallel comprehension of the form: </para>
845 [ e | p1 <- e11, p2 <- e12, ...
846 | q1 <- e21, q2 <- e22, ...
851 <para>This will be translated to: </para>
854 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
855 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
860 <para>where `zipN' is the appropriate zip for the given number of
865 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
867 <sect2 id="generalised-list-comprehensions">
868 <title>Generalised (SQL-Like) List Comprehensions</title>
869 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
871 <indexterm><primary>extended list comprehensions</primary>
873 <indexterm><primary>group</primary></indexterm>
874 <indexterm><primary>sql</primary></indexterm>
877 <para>Generalised list comprehensions are a further enhancement to the
878 list comprehension syntatic sugar to allow operations such as sorting
879 and grouping which are familiar from SQL. They are fully described in the
880 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
881 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
882 except that the syntax we use differs slightly from the paper.</para>
883 <para>Here is an example:
885 employees = [ ("Simon", "MS", 80)
886 , ("Erik", "MS", 100)
888 , ("Gordon", "Ed", 45)
889 , ("Paul", "Yale", 60)]
891 output = [ (the dept, sum salary)
892 | (name, dept, salary) <- employees
894 , then sortWith by (sum salary)
897 In this example, the list <literal>output</literal> would take on
901 [("Yale", 60), ("Ed", 85), ("MS", 180)]
904 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
905 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
906 function that is exported by <literal>GHC.Exts</literal>.)</para>
908 <para>There are five new forms of comprehension qualifier,
909 all introduced by the (existing) keyword <literal>then</literal>:
917 This statement requires that <literal>f</literal> have the type <literal>
918 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
919 motivating example, as this form is used to apply <literal>take 5</literal>.
930 This form is similar to the previous one, but allows you to create a function
931 which will be passed as the first argument to f. As a consequence f must have
932 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
933 from the type, this function lets f "project out" some information
934 from the elements of the list it is transforming.</para>
936 <para>An example is shown in the opening example, where <literal>sortWith</literal>
937 is supplied with a function that lets it find out the <literal>sum salary</literal>
938 for any item in the list comprehension it transforms.</para>
946 then group by e using f
949 <para>This is the most general of the grouping-type statements. In this form,
950 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
951 As with the <literal>then f by e</literal> case above, the first argument
952 is a function supplied to f by the compiler which lets it compute e on every
953 element of the list being transformed. However, unlike the non-grouping case,
954 f additionally partitions the list into a number of sublists: this means that
955 at every point after this statement, binders occurring before it in the comprehension
956 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
957 this, let's look at an example:</para>
960 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
961 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
962 groupRuns f = groupBy (\x y -> f x == f y)
964 output = [ (the x, y)
965 | x <- ([1..3] ++ [1..2])
967 , then group by x using groupRuns ]
970 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
973 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
976 <para>Note that we have used the <literal>the</literal> function to change the type
977 of x from a list to its original numeric type. The variable y, in contrast, is left
978 unchanged from the list form introduced by the grouping.</para>
988 <para>This form of grouping is essentially the same as the one described above. However,
989 since no function to use for the grouping has been supplied it will fall back on the
990 <literal>groupWith</literal> function defined in
991 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
992 is the form of the group statement that we made use of in the opening example.</para>
1003 <para>With this form of the group statement, f is required to simply have the type
1004 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1005 comprehension so far directly. An example of this form is as follows:</para>
1011 , then group using inits]
1014 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1017 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1025 <!-- ===================== REBINDABLE SYNTAX =================== -->
1027 <sect2 id="rebindable-syntax">
1028 <title>Rebindable syntax and the implicit Prelude import</title>
1030 <para><indexterm><primary>-XNoImplicitPrelude
1031 option</primary></indexterm> GHC normally imports
1032 <filename>Prelude.hi</filename> files for you. If you'd
1033 rather it didn't, then give it a
1034 <option>-XNoImplicitPrelude</option> option. The idea is
1035 that you can then import a Prelude of your own. (But don't
1036 call it <literal>Prelude</literal>; the Haskell module
1037 namespace is flat, and you must not conflict with any
1038 Prelude module.)</para>
1040 <para>Suppose you are importing a Prelude of your own
1041 in order to define your own numeric class
1042 hierarchy. It completely defeats that purpose if the
1043 literal "1" means "<literal>Prelude.fromInteger
1044 1</literal>", which is what the Haskell Report specifies.
1045 So the <option>-XNoImplicitPrelude</option>
1046 flag <emphasis>also</emphasis> causes
1047 the following pieces of built-in syntax to refer to
1048 <emphasis>whatever is in scope</emphasis>, not the Prelude
1052 <para>An integer literal <literal>368</literal> means
1053 "<literal>fromInteger (368::Integer)</literal>", rather than
1054 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1057 <listitem><para>Fractional literals are handed in just the same way,
1058 except that the translation is
1059 <literal>fromRational (3.68::Rational)</literal>.
1062 <listitem><para>The equality test in an overloaded numeric pattern
1063 uses whatever <literal>(==)</literal> is in scope.
1066 <listitem><para>The subtraction operation, and the
1067 greater-than-or-equal test, in <literal>n+k</literal> patterns
1068 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1072 <para>Negation (e.g. "<literal>- (f x)</literal>")
1073 means "<literal>negate (f x)</literal>", both in numeric
1074 patterns, and expressions.
1078 <para>"Do" notation is translated using whatever
1079 functions <literal>(>>=)</literal>,
1080 <literal>(>>)</literal>, and <literal>fail</literal>,
1081 are in scope (not the Prelude
1082 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1083 comprehensions, are unaffected. </para></listitem>
1087 notation (see <xref linkend="arrow-notation"/>)
1088 uses whatever <literal>arr</literal>,
1089 <literal>(>>>)</literal>, <literal>first</literal>,
1090 <literal>app</literal>, <literal>(|||)</literal> and
1091 <literal>loop</literal> functions are in scope. But unlike the
1092 other constructs, the types of these functions must match the
1093 Prelude types very closely. Details are in flux; if you want
1097 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1098 even if that is a little unexpected. For example, the
1099 static semantics of the literal <literal>368</literal>
1100 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1101 <literal>fromInteger</literal> to have any of the types:
1103 fromInteger :: Integer -> Integer
1104 fromInteger :: forall a. Foo a => Integer -> a
1105 fromInteger :: Num a => a -> Integer
1106 fromInteger :: Integer -> Bool -> Bool
1110 <para>Be warned: this is an experimental facility, with
1111 fewer checks than usual. Use <literal>-dcore-lint</literal>
1112 to typecheck the desugared program. If Core Lint is happy
1113 you should be all right.</para>
1117 <sect2 id="postfix-operators">
1118 <title>Postfix operators</title>
1121 GHC allows a small extension to the syntax of left operator sections, which
1122 allows you to define postfix operators. The extension is this: the left section
1126 is equivalent (from the point of view of both type checking and execution) to the expression
1130 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1131 The strict Haskell 98 interpretation is that the section is equivalent to
1135 That is, the operator must be a function of two arguments. GHC allows it to
1136 take only one argument, and that in turn allows you to write the function
1139 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1140 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1141 change their behaviour, of course.)
1143 <para>The extension does not extend to the left-hand side of function
1144 definitions; you must define such a function in prefix form.</para>
1148 <sect2 id="disambiguate-fields">
1149 <title>Record field disambiguation</title>
1151 In record construction and record pattern matching
1152 it is entirely unambiguous which field is referred to, even if there are two different
1153 data types in scope with a common field name. For example:
1156 data S = MkS { x :: Int, y :: Bool }
1161 data T = MkT { x :: Int }
1163 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1165 ok2 n = MkT { x = n+1 } -- Unambiguous
1167 bad1 k = k { x = 3 } -- Ambiguous
1168 bad2 k = x k -- Ambiguous
1170 Even though there are two <literal>x</literal>'s in scope,
1171 it is clear that the <literal>x</literal> in the pattern in the
1172 definition of <literal>ok1</literal> can only mean the field
1173 <literal>x</literal> from type <literal>S</literal>. Similarly for
1174 the function <literal>ok2</literal>. However, in the record update
1175 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1176 it is not clear which of the two types is intended.
1179 Haskell 98 regards all four as ambiguous, but with the
1180 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1181 the former two. The rules are precisely the same as those for instance
1182 declarations in Haskell 98, where the method names on the left-hand side
1183 of the method bindings in an instance declaration refer unambiguously
1184 to the method of that class (provided they are in scope at all), even
1185 if there are other variables in scope with the same name.
1186 This reduces the clutter of qualified names when you import two
1187 records from different modules that use the same field name.
1191 <!-- ===================== Record puns =================== -->
1193 <sect2 id="record-puns">
1198 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1202 When using records, it is common to write a pattern that binds a
1203 variable with the same name as a record field, such as:
1206 data C = C {a :: Int}
1212 Record punning permits the variable name to be elided, so one can simply
1219 to mean the same pattern as above. That is, in a record pattern, the
1220 pattern <literal>a</literal> expands into the pattern <literal>a =
1221 a</literal> for the same name <literal>a</literal>.
1225 Note that puns and other patterns can be mixed in the same record:
1227 data C = C {a :: Int, b :: Int}
1228 f (C {a, b = 4}) = a
1230 and that puns can be used wherever record patterns occur (e.g. in
1231 <literal>let</literal> bindings or at the top-level).
1235 Record punning can also be used in an expression, writing, for example,
1241 let a = 1 in C {a = a}
1244 Note that this expansion is purely syntactic, so the record pun
1245 expression refers to the nearest enclosing variable that is spelled the
1246 same as the field name.
1251 <!-- ===================== Record wildcards =================== -->
1253 <sect2 id="record-wildcards">
1254 <title>Record wildcards
1258 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1262 For records with many fields, it can be tiresome to write out each field
1263 individually in a record pattern, as in
1265 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1266 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1271 Record wildcard syntax permits a (<literal>..</literal>) in a record
1272 pattern, where each elided field <literal>f</literal> is replaced by the
1273 pattern <literal>f = f</literal>. For example, the above pattern can be
1276 f (C {a = 1, ..}) = b + c + d
1281 Note that wildcards can be mixed with other patterns, including puns
1282 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1283 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1284 wherever record patterns occur, including in <literal>let</literal>
1285 bindings and at the top-level. For example, the top-level binding
1289 defines <literal>b</literal>, <literal>c</literal>, and
1290 <literal>d</literal>.
1294 Record wildcards can also be used in expressions, writing, for example,
1297 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1303 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1306 Note that this expansion is purely syntactic, so the record wildcard
1307 expression refers to the nearest enclosing variables that are spelled
1308 the same as the omitted field names.
1313 <!-- ===================== Local fixity declarations =================== -->
1315 <sect2 id="local-fixity-declarations">
1316 <title>Local Fixity Declarations
1319 <para>A careful reading of the Haskell 98 Report reveals that fixity
1320 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1321 <literal>infixr</literal>) are permitted to appear inside local bindings
1322 such those introduced by <literal>let</literal> and
1323 <literal>where</literal>. However, the Haskell Report does not specify
1324 the semantics of such bindings very precisely.
1327 <para>In GHC, a fixity declaration may accompany a local binding:
1334 and the fixity declaration applies wherever the binding is in scope.
1335 For example, in a <literal>let</literal>, it applies in the right-hand
1336 sides of other <literal>let</literal>-bindings and the body of the
1337 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1338 expressions (<xref linkend="mdo-notation"/>), the local fixity
1339 declarations of a <literal>let</literal> statement scope over other
1340 statements in the group, just as the bound name does.
1344 Moreover, a local fixity declaration *must* accompany a local binding of
1345 that name: it is not possible to revise the fixity of name bound
1348 let infixr 9 $ in ...
1351 Because local fixity declarations are technically Haskell 98, no flag is
1352 necessary to enable them.
1356 <sect2 id="package-imports">
1357 <title>Package-qualified imports</title>
1359 <para>With the <option>-XPackageImports</option> flag, GHC allows
1360 import declarations to be qualified by the package name that the
1361 module is intended to be imported from. For example:</para>
1364 import "network" Network.Socket
1367 <para>would import the module <literal>Network.Socket</literal> from
1368 the package <literal>network</literal> (any version). This may
1369 be used to disambiguate an import when the same module is
1370 available from multiple packages, or is present in both the
1371 current package being built and an external package.</para>
1373 <para>Note: you probably don't need to use this feature, it was
1374 added mainly so that we can build backwards-compatible versions of
1375 packages when APIs change. It can lead to fragile dependencies in
1376 the common case: modules occasionally move from one package to
1377 another, rendering any package-qualified imports broken.</para>
1380 <sect2 id="syntax-stolen">
1381 <title>Summary of stolen syntax</title>
1383 <para>Turning on an option that enables special syntax
1384 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1385 to compile, perhaps because it uses a variable name which has
1386 become a reserved word. This section lists the syntax that is
1387 "stolen" by language extensions.
1389 notation and nonterminal names from the Haskell 98 lexical syntax
1390 (see the Haskell 98 Report).
1391 We only list syntax changes here that might affect
1392 existing working programs (i.e. "stolen" syntax). Many of these
1393 extensions will also enable new context-free syntax, but in all
1394 cases programs written to use the new syntax would not be
1395 compilable without the option enabled.</para>
1397 <para>There are two classes of special
1402 <para>New reserved words and symbols: character sequences
1403 which are no longer available for use as identifiers in the
1407 <para>Other special syntax: sequences of characters that have
1408 a different meaning when this particular option is turned
1413 The following syntax is stolen:
1418 <literal>forall</literal>
1419 <indexterm><primary><literal>forall</literal></primary></indexterm>
1422 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1423 <option>-XLiberalTypeSynonyms</option>,
1424 <option>-XRank2Types</option>,
1425 <option>-XRankNTypes</option>,
1426 <option>-XPolymorphicComponents</option>,
1427 <option>-XExistentialQuantification</option>
1433 <literal>mdo</literal>
1434 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1437 Stolen by: <option>-XRecursiveDo</option>,
1443 <literal>foreign</literal>
1444 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1447 Stolen by: <option>-XForeignFunctionInterface</option>,
1453 <literal>rec</literal>,
1454 <literal>proc</literal>, <literal>-<</literal>,
1455 <literal>>-</literal>, <literal>-<<</literal>,
1456 <literal>>>-</literal>, and <literal>(|</literal>,
1457 <literal>|)</literal> brackets
1458 <indexterm><primary><literal>proc</literal></primary></indexterm>
1461 Stolen by: <option>-XArrows</option>,
1467 <literal>?<replaceable>varid</replaceable></literal>,
1468 <literal>%<replaceable>varid</replaceable></literal>
1469 <indexterm><primary>implicit parameters</primary></indexterm>
1472 Stolen by: <option>-XImplicitParams</option>,
1478 <literal>[|</literal>,
1479 <literal>[e|</literal>, <literal>[p|</literal>,
1480 <literal>[d|</literal>, <literal>[t|</literal>,
1481 <literal>$(</literal>,
1482 <literal>$<replaceable>varid</replaceable></literal>
1483 <indexterm><primary>Template Haskell</primary></indexterm>
1486 Stolen by: <option>-XTemplateHaskell</option>,
1492 <literal>[:<replaceable>varid</replaceable>|</literal>
1493 <indexterm><primary>quasi-quotation</primary></indexterm>
1496 Stolen by: <option>-XQuasiQuotes</option>,
1502 <replaceable>varid</replaceable>{<literal>#</literal>},
1503 <replaceable>char</replaceable><literal>#</literal>,
1504 <replaceable>string</replaceable><literal>#</literal>,
1505 <replaceable>integer</replaceable><literal>#</literal>,
1506 <replaceable>float</replaceable><literal>#</literal>,
1507 <replaceable>float</replaceable><literal>##</literal>,
1508 <literal>(#</literal>, <literal>#)</literal>,
1511 Stolen by: <option>-XMagicHash</option>,
1520 <!-- TYPE SYSTEM EXTENSIONS -->
1521 <sect1 id="data-type-extensions">
1522 <title>Extensions to data types and type synonyms</title>
1524 <sect2 id="nullary-types">
1525 <title>Data types with no constructors</title>
1527 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1528 a data type with no constructors. For example:</para>
1532 data T a -- T :: * -> *
1535 <para>Syntactically, the declaration lacks the "= constrs" part. The
1536 type can be parameterised over types of any kind, but if the kind is
1537 not <literal>*</literal> then an explicit kind annotation must be used
1538 (see <xref linkend="kinding"/>).</para>
1540 <para>Such data types have only one value, namely bottom.
1541 Nevertheless, they can be useful when defining "phantom types".</para>
1544 <sect2 id="infix-tycons">
1545 <title>Infix type constructors, classes, and type variables</title>
1548 GHC allows type constructors, classes, and type variables to be operators, and
1549 to be written infix, very much like expressions. More specifically:
1552 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1553 The lexical syntax is the same as that for data constructors.
1556 Data type and type-synonym declarations can be written infix, parenthesised
1557 if you want further arguments. E.g.
1559 data a :*: b = Foo a b
1560 type a :+: b = Either a b
1561 class a :=: b where ...
1563 data (a :**: b) x = Baz a b x
1564 type (a :++: b) y = Either (a,b) y
1568 Types, and class constraints, can be written infix. For example
1571 f :: (a :=: b) => a -> b
1575 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1576 The lexical syntax is the same as that for variable operators, excluding "(.)",
1577 "(!)", and "(*)". In a binding position, the operator must be
1578 parenthesised. For example:
1580 type T (+) = Int + Int
1584 liftA2 :: Arrow (~>)
1585 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1591 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1592 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1595 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1596 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1597 sets the fixity for a data constructor and the corresponding type constructor. For example:
1601 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1602 and similarly for <literal>:*:</literal>.
1603 <literal>Int `a` Bool</literal>.
1606 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1613 <sect2 id="type-synonyms">
1614 <title>Liberalised type synonyms</title>
1617 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1618 on individual synonym declarations.
1619 With the <option>-XLiberalTypeSynonyms</option> extension,
1620 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1621 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1624 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1625 in a type synonym, thus:
1627 type Discard a = forall b. Show b => a -> b -> (a, String)
1632 g :: Discard Int -> (Int,String) -- A rank-2 type
1639 If you also use <option>-XUnboxedTuples</option>,
1640 you can write an unboxed tuple in a type synonym:
1642 type Pr = (# Int, Int #)
1650 You can apply a type synonym to a forall type:
1652 type Foo a = a -> a -> Bool
1654 f :: Foo (forall b. b->b)
1656 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1658 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1663 You can apply a type synonym to a partially applied type synonym:
1665 type Generic i o = forall x. i x -> o x
1668 foo :: Generic Id []
1670 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1672 foo :: forall x. x -> [x]
1680 GHC currently does kind checking before expanding synonyms (though even that
1684 After expanding type synonyms, GHC does validity checking on types, looking for
1685 the following mal-formedness which isn't detected simply by kind checking:
1688 Type constructor applied to a type involving for-alls.
1691 Unboxed tuple on left of an arrow.
1694 Partially-applied type synonym.
1698 this will be rejected:
1700 type Pr = (# Int, Int #)
1705 because GHC does not allow unboxed tuples on the left of a function arrow.
1710 <sect2 id="existential-quantification">
1711 <title>Existentially quantified data constructors
1715 The idea of using existential quantification in data type declarations
1716 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1717 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1718 London, 1991). It was later formalised by Laufer and Odersky
1719 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1720 TOPLAS, 16(5), pp1411-1430, 1994).
1721 It's been in Lennart
1722 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1723 proved very useful. Here's the idea. Consider the declaration:
1729 data Foo = forall a. MkFoo a (a -> Bool)
1736 The data type <literal>Foo</literal> has two constructors with types:
1742 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1749 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1750 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1751 For example, the following expression is fine:
1757 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1763 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1764 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1765 isUpper</function> packages a character with a compatible function. These
1766 two things are each of type <literal>Foo</literal> and can be put in a list.
1770 What can we do with a value of type <literal>Foo</literal>?. In particular,
1771 what happens when we pattern-match on <function>MkFoo</function>?
1777 f (MkFoo val fn) = ???
1783 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1784 are compatible, the only (useful) thing we can do with them is to
1785 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1792 f (MkFoo val fn) = fn val
1798 What this allows us to do is to package heterogeneous values
1799 together with a bunch of functions that manipulate them, and then treat
1800 that collection of packages in a uniform manner. You can express
1801 quite a bit of object-oriented-like programming this way.
1804 <sect3 id="existential">
1805 <title>Why existential?
1809 What has this to do with <emphasis>existential</emphasis> quantification?
1810 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1816 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1822 But Haskell programmers can safely think of the ordinary
1823 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1824 adding a new existential quantification construct.
1829 <sect3 id="existential-with-context">
1830 <title>Existentials and type classes</title>
1833 An easy extension is to allow
1834 arbitrary contexts before the constructor. For example:
1840 data Baz = forall a. Eq a => Baz1 a a
1841 | forall b. Show b => Baz2 b (b -> b)
1847 The two constructors have the types you'd expect:
1853 Baz1 :: forall a. Eq a => a -> a -> Baz
1854 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1860 But when pattern matching on <function>Baz1</function> the matched values can be compared
1861 for equality, and when pattern matching on <function>Baz2</function> the first matched
1862 value can be converted to a string (as well as applying the function to it).
1863 So this program is legal:
1870 f (Baz1 p q) | p == q = "Yes"
1872 f (Baz2 v fn) = show (fn v)
1878 Operationally, in a dictionary-passing implementation, the
1879 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1880 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1881 extract it on pattern matching.
1886 <sect3 id="existential-records">
1887 <title>Record Constructors</title>
1890 GHC allows existentials to be used with records syntax as well. For example:
1893 data Counter a = forall self. NewCounter
1895 , _inc :: self -> self
1896 , _display :: self -> IO ()
1900 Here <literal>tag</literal> is a public field, with a well-typed selector
1901 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1902 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1903 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1904 compile-time error. In other words, <emphasis>GHC defines a record selector function
1905 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1906 (This example used an underscore in the fields for which record selectors
1907 will not be defined, but that is only programming style; GHC ignores them.)
1911 To make use of these hidden fields, we need to create some helper functions:
1914 inc :: Counter a -> Counter a
1915 inc (NewCounter x i d t) = NewCounter
1916 { _this = i x, _inc = i, _display = d, tag = t }
1918 display :: Counter a -> IO ()
1919 display NewCounter{ _this = x, _display = d } = d x
1922 Now we can define counters with different underlying implementations:
1925 counterA :: Counter String
1926 counterA = NewCounter
1927 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1929 counterB :: Counter String
1930 counterB = NewCounter
1931 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1934 display (inc counterA) -- prints "1"
1935 display (inc (inc counterB)) -- prints "##"
1938 At the moment, record update syntax is only supported for Haskell 98 data types,
1939 so the following function does <emphasis>not</emphasis> work:
1942 -- This is invalid; use explicit NewCounter instead for now
1943 setTag :: Counter a -> a -> Counter a
1944 setTag obj t = obj{ tag = t }
1953 <title>Restrictions</title>
1956 There are several restrictions on the ways in which existentially-quantified
1957 constructors can be use.
1966 When pattern matching, each pattern match introduces a new,
1967 distinct, type for each existential type variable. These types cannot
1968 be unified with any other type, nor can they escape from the scope of
1969 the pattern match. For example, these fragments are incorrect:
1977 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1978 is the result of <function>f1</function>. One way to see why this is wrong is to
1979 ask what type <function>f1</function> has:
1983 f1 :: Foo -> a -- Weird!
1987 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1992 f1 :: forall a. Foo -> a -- Wrong!
1996 The original program is just plain wrong. Here's another sort of error
2000 f2 (Baz1 a b) (Baz1 p q) = a==q
2004 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2005 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2006 from the two <function>Baz1</function> constructors.
2014 You can't pattern-match on an existentially quantified
2015 constructor in a <literal>let</literal> or <literal>where</literal> group of
2016 bindings. So this is illegal:
2020 f3 x = a==b where { Baz1 a b = x }
2023 Instead, use a <literal>case</literal> expression:
2026 f3 x = case x of Baz1 a b -> a==b
2029 In general, you can only pattern-match
2030 on an existentially-quantified constructor in a <literal>case</literal> expression or
2031 in the patterns of a function definition.
2033 The reason for this restriction is really an implementation one.
2034 Type-checking binding groups is already a nightmare without
2035 existentials complicating the picture. Also an existential pattern
2036 binding at the top level of a module doesn't make sense, because it's
2037 not clear how to prevent the existentially-quantified type "escaping".
2038 So for now, there's a simple-to-state restriction. We'll see how
2046 You can't use existential quantification for <literal>newtype</literal>
2047 declarations. So this is illegal:
2051 newtype T = forall a. Ord a => MkT a
2055 Reason: a value of type <literal>T</literal> must be represented as a
2056 pair of a dictionary for <literal>Ord t</literal> and a value of type
2057 <literal>t</literal>. That contradicts the idea that
2058 <literal>newtype</literal> should have no concrete representation.
2059 You can get just the same efficiency and effect by using
2060 <literal>data</literal> instead of <literal>newtype</literal>. If
2061 there is no overloading involved, then there is more of a case for
2062 allowing an existentially-quantified <literal>newtype</literal>,
2063 because the <literal>data</literal> version does carry an
2064 implementation cost, but single-field existentially quantified
2065 constructors aren't much use. So the simple restriction (no
2066 existential stuff on <literal>newtype</literal>) stands, unless there
2067 are convincing reasons to change it.
2075 You can't use <literal>deriving</literal> to define instances of a
2076 data type with existentially quantified data constructors.
2078 Reason: in most cases it would not make sense. For example:;
2081 data T = forall a. MkT [a] deriving( Eq )
2084 To derive <literal>Eq</literal> in the standard way we would need to have equality
2085 between the single component of two <function>MkT</function> constructors:
2089 (MkT a) == (MkT b) = ???
2092 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2093 It's just about possible to imagine examples in which the derived instance
2094 would make sense, but it seems altogether simpler simply to prohibit such
2095 declarations. Define your own instances!
2106 <!-- ====================== Generalised algebraic data types ======================= -->
2108 <sect2 id="gadt-style">
2109 <title>Declaring data types with explicit constructor signatures</title>
2111 <para>GHC allows you to declare an algebraic data type by
2112 giving the type signatures of constructors explicitly. For example:
2116 Just :: a -> Maybe a
2118 The form is called a "GADT-style declaration"
2119 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2120 can only be declared using this form.</para>
2121 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2122 For example, these two declarations are equivalent:
2124 data Foo = forall a. MkFoo a (a -> Bool)
2125 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2128 <para>Any data type that can be declared in standard Haskell-98 syntax
2129 can also be declared using GADT-style syntax.
2130 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2131 they treat class constraints on the data constructors differently.
2132 Specifically, if the constructor is given a type-class context, that
2133 context is made available by pattern matching. For example:
2136 MkSet :: Eq a => [a] -> Set a
2138 makeSet :: Eq a => [a] -> Set a
2139 makeSet xs = MkSet (nub xs)
2141 insert :: a -> Set a -> Set a
2142 insert a (MkSet as) | a `elem` as = MkSet as
2143 | otherwise = MkSet (a:as)
2145 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2146 gives rise to a <literal>(Eq a)</literal>
2147 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2148 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2149 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2150 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2151 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2152 In the example, the equality dictionary is used to satisfy the equality constraint
2153 generated by the call to <literal>elem</literal>, so that the type of
2154 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2157 For example, one possible application is to reify dictionaries:
2159 data NumInst a where
2160 MkNumInst :: Num a => NumInst a
2162 intInst :: NumInst Int
2165 plus :: NumInst a -> a -> a -> a
2166 plus MkNumInst p q = p + q
2168 Here, a value of type <literal>NumInst a</literal> is equivalent
2169 to an explicit <literal>(Num a)</literal> dictionary.
2172 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2173 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2177 = Num a => MkNumInst (NumInst a)
2179 Notice that, unlike the situation when declaring an existential, there is
2180 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2181 data type's universally quantified type variable <literal>a</literal>.
2182 A constructor may have both universal and existential type variables: for example,
2183 the following two declarations are equivalent:
2186 = forall b. (Num a, Eq b) => MkT1 a b
2188 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2191 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2192 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2193 In Haskell 98 the definition
2195 data Eq a => Set' a = MkSet' [a]
2197 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2198 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2199 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2200 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2201 GHC's behaviour is much more useful, as well as much more intuitive.
2205 The rest of this section gives further details about GADT-style data
2210 The result type of each data constructor must begin with the type constructor being defined.
2211 If the result type of all constructors
2212 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2213 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2214 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2218 The type signature of
2219 each constructor is independent, and is implicitly universally quantified as usual.
2220 Different constructors may have different universally-quantified type variables
2221 and different type-class constraints.
2222 For example, this is fine:
2225 T1 :: Eq b => b -> T b
2226 T2 :: (Show c, Ix c) => c -> [c] -> T c
2231 Unlike a Haskell-98-style
2232 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2233 have no scope. Indeed, one can write a kind signature instead:
2235 data Set :: * -> * where ...
2237 or even a mixture of the two:
2239 data Foo a :: (* -> *) -> * where ...
2241 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2244 data Foo a (b :: * -> *) where ...
2250 You can use strictness annotations, in the obvious places
2251 in the constructor type:
2254 Lit :: !Int -> Term Int
2255 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2256 Pair :: Term a -> Term b -> Term (a,b)
2261 You can use a <literal>deriving</literal> clause on a GADT-style data type
2262 declaration. For example, these two declarations are equivalent
2264 data Maybe1 a where {
2265 Nothing1 :: Maybe1 a ;
2266 Just1 :: a -> Maybe1 a
2267 } deriving( Eq, Ord )
2269 data Maybe2 a = Nothing2 | Just2 a
2275 You can use record syntax on a GADT-style data type declaration:
2279 Adult { name :: String, children :: [Person] } :: Person
2280 Child { name :: String } :: Person
2282 As usual, for every constructor that has a field <literal>f</literal>, the type of
2283 field <literal>f</literal> must be the same (modulo alpha conversion).
2286 At the moment, record updates are not yet possible with GADT-style declarations,
2287 so support is limited to record construction, selection and pattern matching.
2290 aPerson = Adult { name = "Fred", children = [] }
2292 shortName :: Person -> Bool
2293 hasChildren (Adult { children = kids }) = not (null kids)
2294 hasChildren (Child {}) = False
2299 As in the case of existentials declared using the Haskell-98-like record syntax
2300 (<xref linkend="existential-records"/>),
2301 record-selector functions are generated only for those fields that have well-typed
2303 Here is the example of that section, in GADT-style syntax:
2305 data Counter a where
2306 NewCounter { _this :: self
2307 , _inc :: self -> self
2308 , _display :: self -> IO ()
2313 As before, only one selector function is generated here, that for <literal>tag</literal>.
2314 Nevertheless, you can still use all the field names in pattern matching and record construction.
2316 </itemizedlist></para>
2320 <title>Generalised Algebraic Data Types (GADTs)</title>
2322 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2323 by allowing constructors to have richer return types. Here is an example:
2326 Lit :: Int -> Term Int
2327 Succ :: Term Int -> Term Int
2328 IsZero :: Term Int -> Term Bool
2329 If :: Term Bool -> Term a -> Term a -> Term a
2330 Pair :: Term a -> Term b -> Term (a,b)
2332 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2333 case with ordinary data types. This generality allows us to
2334 write a well-typed <literal>eval</literal> function
2335 for these <literal>Terms</literal>:
2339 eval (Succ t) = 1 + eval t
2340 eval (IsZero t) = eval t == 0
2341 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2342 eval (Pair e1 e2) = (eval e1, eval e2)
2344 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2345 For example, in the right hand side of the equation
2350 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2351 A precise specification of the type rules is beyond what this user manual aspires to,
2352 but the design closely follows that described in
2354 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2355 unification-based type inference for GADTs</ulink>,
2357 The general principle is this: <emphasis>type refinement is only carried out
2358 based on user-supplied type annotations</emphasis>.
2359 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2360 and lots of obscure error messages will
2361 occur. However, the refinement is quite general. For example, if we had:
2363 eval :: Term a -> a -> a
2364 eval (Lit i) j = i+j
2366 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2367 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2368 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2371 These and many other examples are given in papers by Hongwei Xi, and
2372 Tim Sheard. There is a longer introduction
2373 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2375 <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
2376 may use different notation to that implemented in GHC.
2379 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2380 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2383 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2384 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2385 The result type of each constructor must begin with the type constructor being defined,
2386 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2387 For example, in the <literal>Term</literal> data
2388 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2389 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2394 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2395 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2396 whose result type is not just <literal>T a b</literal>.
2400 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2401 an ordinary data type.
2405 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2409 Lit { val :: Int } :: Term Int
2410 Succ { num :: Term Int } :: Term Int
2411 Pred { num :: Term Int } :: Term Int
2412 IsZero { arg :: Term Int } :: Term Bool
2413 Pair { arg1 :: Term a
2416 If { cnd :: Term Bool
2421 However, for GADTs there is the following additional constraint:
2422 every constructor that has a field <literal>f</literal> must have
2423 the same result type (modulo alpha conversion)
2424 Hence, in the above example, we cannot merge the <literal>num</literal>
2425 and <literal>arg</literal> fields above into a
2426 single name. Although their field types are both <literal>Term Int</literal>,
2427 their selector functions actually have different types:
2430 num :: Term Int -> Term Int
2431 arg :: Term Bool -> Term Int
2436 When pattern-matching against data constructors drawn from a GADT,
2437 for example in a <literal>case</literal> expression, the following rules apply:
2439 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2440 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2441 <listitem><para>The type of any free variable mentioned in any of
2442 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2444 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2445 way to ensure that a variable a rigid type is to give it a type signature.
2446 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2447 Simple unification-based type inference for GADTs
2448 </ulink>. The criteria implemented by GHC are given in the Appendix.
2458 <!-- ====================== End of Generalised algebraic data types ======================= -->
2460 <sect1 id="deriving">
2461 <title>Extensions to the "deriving" mechanism</title>
2463 <sect2 id="deriving-inferred">
2464 <title>Inferred context for deriving clauses</title>
2467 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2470 data T0 f a = MkT0 a deriving( Eq )
2471 data T1 f a = MkT1 (f a) deriving( Eq )
2472 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2474 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2476 instance Eq a => Eq (T0 f a) where ...
2477 instance Eq (f a) => Eq (T1 f a) where ...
2478 instance Eq (f (f a)) => Eq (T2 f a) where ...
2480 The first of these is obviously fine. The second is still fine, although less obviously.
2481 The third is not Haskell 98, and risks losing termination of instances.
2484 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2485 each constraint in the inferred instance context must consist only of type variables,
2486 with no repetitions.
2489 This rule is applied regardless of flags. If you want a more exotic context, you can write
2490 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2494 <sect2 id="stand-alone-deriving">
2495 <title>Stand-alone deriving declarations</title>
2498 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2500 data Foo a = Bar a | Baz String
2502 deriving instance Eq a => Eq (Foo a)
2504 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2505 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2506 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2507 exactly as you would in an ordinary instance declaration.
2508 (In contrast the context is inferred in a <literal>deriving</literal> clause
2509 attached to a data type declaration.)
2511 A <literal>deriving instance</literal> declaration
2512 must obey the same rules concerning form and termination as ordinary instance declarations,
2513 controlled by the same flags; see <xref linkend="instance-decls"/>.
2516 Unlike a <literal>deriving</literal>
2517 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2518 than the data type (assuming you also use
2519 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2522 data Foo a = Bar a | Baz String
2524 deriving instance Eq a => Eq (Foo [a])
2525 deriving instance Eq a => Eq (Foo (Maybe a))
2527 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2528 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2531 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2532 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2535 newtype Foo a = MkFoo (State Int a)
2537 deriving instance MonadState Int Foo
2539 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2540 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2546 <sect2 id="deriving-typeable">
2547 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2550 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2551 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2552 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2553 classes <literal>Eq</literal>, <literal>Ord</literal>,
2554 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2557 GHC extends this list with two more classes that may be automatically derived
2558 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2559 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2560 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2561 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2563 <para>An instance of <literal>Typeable</literal> can only be derived if the
2564 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2565 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2567 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2568 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2570 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2571 are used, and only <literal>Typeable1</literal> up to
2572 <literal>Typeable7</literal> are provided in the library.)
2573 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2574 class, whose kind suits that of the data type constructor, and
2575 then writing the data type instance by hand.
2579 <sect2 id="newtype-deriving">
2580 <title>Generalised derived instances for newtypes</title>
2583 When you define an abstract type using <literal>newtype</literal>, you may want
2584 the new type to inherit some instances from its representation. In
2585 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2586 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2587 other classes you have to write an explicit instance declaration. For
2588 example, if you define
2591 newtype Dollars = Dollars Int
2594 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2595 explicitly define an instance of <literal>Num</literal>:
2598 instance Num Dollars where
2599 Dollars a + Dollars b = Dollars (a+b)
2602 All the instance does is apply and remove the <literal>newtype</literal>
2603 constructor. It is particularly galling that, since the constructor
2604 doesn't appear at run-time, this instance declaration defines a
2605 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2606 dictionary, only slower!
2610 <sect3> <title> Generalising the deriving clause </title>
2612 GHC now permits such instances to be derived instead,
2613 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2616 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2619 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2620 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2621 derives an instance declaration of the form
2624 instance Num Int => Num Dollars
2627 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2631 We can also derive instances of constructor classes in a similar
2632 way. For example, suppose we have implemented state and failure monad
2633 transformers, such that
2636 instance Monad m => Monad (State s m)
2637 instance Monad m => Monad (Failure m)
2639 In Haskell 98, we can define a parsing monad by
2641 type Parser tok m a = State [tok] (Failure m) a
2644 which is automatically a monad thanks to the instance declarations
2645 above. With the extension, we can make the parser type abstract,
2646 without needing to write an instance of class <literal>Monad</literal>, via
2649 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2652 In this case the derived instance declaration is of the form
2654 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2657 Notice that, since <literal>Monad</literal> is a constructor class, the
2658 instance is a <emphasis>partial application</emphasis> of the new type, not the
2659 entire left hand side. We can imagine that the type declaration is
2660 "eta-converted" to generate the context of the instance
2665 We can even derive instances of multi-parameter classes, provided the
2666 newtype is the last class parameter. In this case, a ``partial
2667 application'' of the class appears in the <literal>deriving</literal>
2668 clause. For example, given the class
2671 class StateMonad s m | m -> s where ...
2672 instance Monad m => StateMonad s (State s m) where ...
2674 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2676 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2677 deriving (Monad, StateMonad [tok])
2680 The derived instance is obtained by completing the application of the
2681 class to the new type:
2684 instance StateMonad [tok] (State [tok] (Failure m)) =>
2685 StateMonad [tok] (Parser tok m)
2690 As a result of this extension, all derived instances in newtype
2691 declarations are treated uniformly (and implemented just by reusing
2692 the dictionary for the representation type), <emphasis>except</emphasis>
2693 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2694 the newtype and its representation.
2698 <sect3> <title> A more precise specification </title>
2700 Derived instance declarations are constructed as follows. Consider the
2701 declaration (after expansion of any type synonyms)
2704 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2710 The <literal>ci</literal> are partial applications of
2711 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2712 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2715 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2718 The type <literal>t</literal> is an arbitrary type.
2721 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2722 nor in the <literal>ci</literal>, and
2725 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2726 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2727 should not "look through" the type or its constructor. You can still
2728 derive these classes for a newtype, but it happens in the usual way, not
2729 via this new mechanism.
2732 Then, for each <literal>ci</literal>, the derived instance
2735 instance ci t => ci (T v1...vk)
2737 As an example which does <emphasis>not</emphasis> work, consider
2739 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2741 Here we cannot derive the instance
2743 instance Monad (State s m) => Monad (NonMonad m)
2746 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2747 and so cannot be "eta-converted" away. It is a good thing that this
2748 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2749 not, in fact, a monad --- for the same reason. Try defining
2750 <literal>>>=</literal> with the correct type: you won't be able to.
2754 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2755 important, since we can only derive instances for the last one. If the
2756 <literal>StateMonad</literal> class above were instead defined as
2759 class StateMonad m s | m -> s where ...
2762 then we would not have been able to derive an instance for the
2763 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2764 classes usually have one "main" parameter for which deriving new
2765 instances is most interesting.
2767 <para>Lastly, all of this applies only for classes other than
2768 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2769 and <literal>Data</literal>, for which the built-in derivation applies (section
2770 4.3.3. of the Haskell Report).
2771 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2772 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2773 the standard method is used or the one described here.)
2780 <!-- TYPE SYSTEM EXTENSIONS -->
2781 <sect1 id="type-class-extensions">
2782 <title>Class and instances declarations</title>
2784 <sect2 id="multi-param-type-classes">
2785 <title>Class declarations</title>
2788 This section, and the next one, documents GHC's type-class extensions.
2789 There's lots of background in the paper <ulink
2790 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2791 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2792 Jones, Erik Meijer).
2795 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2799 <title>Multi-parameter type classes</title>
2801 Multi-parameter type classes are permitted. For example:
2805 class Collection c a where
2806 union :: c a -> c a -> c a
2814 <title>The superclasses of a class declaration</title>
2817 There are no restrictions on the context in a class declaration
2818 (which introduces superclasses), except that the class hierarchy must
2819 be acyclic. So these class declarations are OK:
2823 class Functor (m k) => FiniteMap m k where
2826 class (Monad m, Monad (t m)) => Transform t m where
2827 lift :: m a -> (t m) a
2833 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2834 of "acyclic" involves only the superclass relationships. For example,
2840 op :: D b => a -> b -> b
2843 class C a => D a where { ... }
2847 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2848 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2849 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2856 <sect3 id="class-method-types">
2857 <title>Class method types</title>
2860 Haskell 98 prohibits class method types to mention constraints on the
2861 class type variable, thus:
2864 fromList :: [a] -> s a
2865 elem :: Eq a => a -> s a -> Bool
2867 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2868 contains the constraint <literal>Eq a</literal>, constrains only the
2869 class type variable (in this case <literal>a</literal>).
2870 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2877 <sect2 id="functional-dependencies">
2878 <title>Functional dependencies
2881 <para> Functional dependencies are implemented as described by Mark Jones
2882 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2883 In Proceedings of the 9th European Symposium on Programming,
2884 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2888 Functional dependencies are introduced by a vertical bar in the syntax of a
2889 class declaration; e.g.
2891 class (Monad m) => MonadState s m | m -> s where ...
2893 class Foo a b c | a b -> c where ...
2895 There should be more documentation, but there isn't (yet). Yell if you need it.
2898 <sect3><title>Rules for functional dependencies </title>
2900 In a class declaration, all of the class type variables must be reachable (in the sense
2901 mentioned in <xref linkend="type-restrictions"/>)
2902 from the free variables of each method type.
2906 class Coll s a where
2908 insert :: s -> a -> s
2911 is not OK, because the type of <literal>empty</literal> doesn't mention
2912 <literal>a</literal>. Functional dependencies can make the type variable
2915 class Coll s a | s -> a where
2917 insert :: s -> a -> s
2920 Alternatively <literal>Coll</literal> might be rewritten
2923 class Coll s a where
2925 insert :: s a -> a -> s a
2929 which makes the connection between the type of a collection of
2930 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2931 Occasionally this really doesn't work, in which case you can split the
2939 class CollE s => Coll s a where
2940 insert :: s -> a -> s
2947 <title>Background on functional dependencies</title>
2949 <para>The following description of the motivation and use of functional dependencies is taken
2950 from the Hugs user manual, reproduced here (with minor changes) by kind
2951 permission of Mark Jones.
2954 Consider the following class, intended as part of a
2955 library for collection types:
2957 class Collects e ce where
2959 insert :: e -> ce -> ce
2960 member :: e -> ce -> Bool
2962 The type variable e used here represents the element type, while ce is the type
2963 of the container itself. Within this framework, we might want to define
2964 instances of this class for lists or characteristic functions (both of which
2965 can be used to represent collections of any equality type), bit sets (which can
2966 be used to represent collections of characters), or hash tables (which can be
2967 used to represent any collection whose elements have a hash function). Omitting
2968 standard implementation details, this would lead to the following declarations:
2970 instance Eq e => Collects e [e] where ...
2971 instance Eq e => Collects e (e -> Bool) where ...
2972 instance Collects Char BitSet where ...
2973 instance (Hashable e, Collects a ce)
2974 => Collects e (Array Int ce) where ...
2976 All this looks quite promising; we have a class and a range of interesting
2977 implementations. Unfortunately, there are some serious problems with the class
2978 declaration. First, the empty function has an ambiguous type:
2980 empty :: Collects e ce => ce
2982 By "ambiguous" we mean that there is a type variable e that appears on the left
2983 of the <literal>=></literal> symbol, but not on the right. The problem with
2984 this is that, according to the theoretical foundations of Haskell overloading,
2985 we cannot guarantee a well-defined semantics for any term with an ambiguous
2989 We can sidestep this specific problem by removing the empty member from the
2990 class declaration. However, although the remaining members, insert and member,
2991 do not have ambiguous types, we still run into problems when we try to use
2992 them. For example, consider the following two functions:
2994 f x y = insert x . insert y
2997 for which GHC infers the following types:
2999 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3000 g :: (Collects Bool c, Collects Char c) => c -> c
3002 Notice that the type for f allows the two parameters x and y to be assigned
3003 different types, even though it attempts to insert each of the two values, one
3004 after the other, into the same collection. If we're trying to model collections
3005 that contain only one type of value, then this is clearly an inaccurate
3006 type. Worse still, the definition for g is accepted, without causing a type
3007 error. As a result, the error in this code will not be flagged at the point
3008 where it appears. Instead, it will show up only when we try to use g, which
3009 might even be in a different module.
3012 <sect4><title>An attempt to use constructor classes</title>
3015 Faced with the problems described above, some Haskell programmers might be
3016 tempted to use something like the following version of the class declaration:
3018 class Collects e c where
3020 insert :: e -> c e -> c e
3021 member :: e -> c e -> Bool
3023 The key difference here is that we abstract over the type constructor c that is
3024 used to form the collection type c e, and not over that collection type itself,
3025 represented by ce in the original class declaration. This avoids the immediate
3026 problems that we mentioned above: empty has type <literal>Collects e c => c
3027 e</literal>, which is not ambiguous.
3030 The function f from the previous section has a more accurate type:
3032 f :: (Collects e c) => e -> e -> c e -> c e
3034 The function g from the previous section is now rejected with a type error as
3035 we would hope because the type of f does not allow the two arguments to have
3037 This, then, is an example of a multiple parameter class that does actually work
3038 quite well in practice, without ambiguity problems.
3039 There is, however, a catch. This version of the Collects class is nowhere near
3040 as general as the original class seemed to be: only one of the four instances
3041 for <literal>Collects</literal>
3042 given above can be used with this version of Collects because only one of
3043 them---the instance for lists---has a collection type that can be written in
3044 the form c e, for some type constructor c, and element type e.
3048 <sect4><title>Adding functional dependencies</title>
3051 To get a more useful version of the Collects class, Hugs provides a mechanism
3052 that allows programmers to specify dependencies between the parameters of a
3053 multiple parameter class (For readers with an interest in theoretical
3054 foundations and previous work: The use of dependency information can be seen
3055 both as a generalization of the proposal for `parametric type classes' that was
3056 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3057 later framework for "improvement" of qualified types. The
3058 underlying ideas are also discussed in a more theoretical and abstract setting
3059 in a manuscript [implparam], where they are identified as one point in a
3060 general design space for systems of implicit parameterization.).
3062 To start with an abstract example, consider a declaration such as:
3064 class C a b where ...
3066 which tells us simply that C can be thought of as a binary relation on types
3067 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3068 included in the definition of classes to add information about dependencies
3069 between parameters, as in the following examples:
3071 class D a b | a -> b where ...
3072 class E a b | a -> b, b -> a where ...
3074 The notation <literal>a -> b</literal> used here between the | and where
3075 symbols --- not to be
3076 confused with a function type --- indicates that the a parameter uniquely
3077 determines the b parameter, and might be read as "a determines b." Thus D is
3078 not just a relation, but actually a (partial) function. Similarly, from the two
3079 dependencies that are included in the definition of E, we can see that E
3080 represents a (partial) one-one mapping between types.
3083 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3084 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3085 m>=0, meaning that the y parameters are uniquely determined by the x
3086 parameters. Spaces can be used as separators if more than one variable appears
3087 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3088 annotated with multiple dependencies using commas as separators, as in the
3089 definition of E above. Some dependencies that we can write in this notation are
3090 redundant, and will be rejected because they don't serve any useful
3091 purpose, and may instead indicate an error in the program. Examples of
3092 dependencies like this include <literal>a -> a </literal>,
3093 <literal>a -> a a </literal>,
3094 <literal>a -> </literal>, etc. There can also be
3095 some redundancy if multiple dependencies are given, as in
3096 <literal>a->b</literal>,
3097 <literal>b->c </literal>, <literal>a->c </literal>, and
3098 in which some subset implies the remaining dependencies. Examples like this are
3099 not treated as errors. Note that dependencies appear only in class
3100 declarations, and not in any other part of the language. In particular, the
3101 syntax for instance declarations, class constraints, and types is completely
3105 By including dependencies in a class declaration, we provide a mechanism for
3106 the programmer to specify each multiple parameter class more precisely. The
3107 compiler, on the other hand, is responsible for ensuring that the set of
3108 instances that are in scope at any given point in the program is consistent
3109 with any declared dependencies. For example, the following pair of instance
3110 declarations cannot appear together in the same scope because they violate the
3111 dependency for D, even though either one on its own would be acceptable:
3113 instance D Bool Int where ...
3114 instance D Bool Char where ...
3116 Note also that the following declaration is not allowed, even by itself:
3118 instance D [a] b where ...
3120 The problem here is that this instance would allow one particular choice of [a]
3121 to be associated with more than one choice for b, which contradicts the
3122 dependency specified in the definition of D. More generally, this means that,
3123 in any instance of the form:
3125 instance D t s where ...
3127 for some particular types t and s, the only variables that can appear in s are
3128 the ones that appear in t, and hence, if the type t is known, then s will be
3129 uniquely determined.
3132 The benefit of including dependency information is that it allows us to define
3133 more general multiple parameter classes, without ambiguity problems, and with
3134 the benefit of more accurate types. To illustrate this, we return to the
3135 collection class example, and annotate the original definition of <literal>Collects</literal>
3136 with a simple dependency:
3138 class Collects e ce | ce -> e where
3140 insert :: e -> ce -> ce
3141 member :: e -> ce -> Bool
3143 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3144 determined by the type of the collection ce. Note that both parameters of
3145 Collects are of kind *; there are no constructor classes here. Note too that
3146 all of the instances of Collects that we gave earlier can be used
3147 together with this new definition.
3150 What about the ambiguity problems that we encountered with the original
3151 definition? The empty function still has type Collects e ce => ce, but it is no
3152 longer necessary to regard that as an ambiguous type: Although the variable e
3153 does not appear on the right of the => symbol, the dependency for class
3154 Collects tells us that it is uniquely determined by ce, which does appear on
3155 the right of the => symbol. Hence the context in which empty is used can still
3156 give enough information to determine types for both ce and e, without
3157 ambiguity. More generally, we need only regard a type as ambiguous if it
3158 contains a variable on the left of the => that is not uniquely determined
3159 (either directly or indirectly) by the variables on the right.
3162 Dependencies also help to produce more accurate types for user defined
3163 functions, and hence to provide earlier detection of errors, and less cluttered
3164 types for programmers to work with. Recall the previous definition for a
3167 f x y = insert x y = insert x . insert y
3169 for which we originally obtained a type:
3171 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3173 Given the dependency information that we have for Collects, however, we can
3174 deduce that a and b must be equal because they both appear as the second
3175 parameter in a Collects constraint with the same first parameter c. Hence we
3176 can infer a shorter and more accurate type for f:
3178 f :: (Collects a c) => a -> a -> c -> c
3180 In a similar way, the earlier definition of g will now be flagged as a type error.
3183 Although we have given only a few examples here, it should be clear that the
3184 addition of dependency information can help to make multiple parameter classes
3185 more useful in practice, avoiding ambiguity problems, and allowing more general
3186 sets of instance declarations.
3192 <sect2 id="instance-decls">
3193 <title>Instance declarations</title>
3195 <sect3 id="instance-rules">
3196 <title>Relaxed rules for instance declarations</title>
3198 <para>An instance declaration has the form
3200 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 ...
3202 The part before the "<literal>=></literal>" is the
3203 <emphasis>context</emphasis>, while the part after the
3204 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3208 In Haskell 98 the head of an instance declaration
3209 must be of the form <literal>C (T a1 ... an)</literal>, where
3210 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3211 and the <literal>a1 ... an</literal> are distinct type variables.
3212 Furthermore, the assertions in the context of the instance declaration
3213 must be of the form <literal>C a</literal> where <literal>a</literal>
3214 is a type variable that occurs in the head.
3217 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3218 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3219 the context and head of the instance declaration can each consist of arbitrary
3220 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3224 The Paterson Conditions: for each assertion in the context
3226 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3227 <listitem><para>The assertion has fewer constructors and variables (taken together
3228 and counting repetitions) than the head</para></listitem>
3232 <listitem><para>The Coverage Condition. For each functional dependency,
3233 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3234 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3235 every type variable in
3236 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3237 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3238 substitution mapping each type variable in the class declaration to the
3239 corresponding type in the instance declaration.
3242 These restrictions ensure that context reduction terminates: each reduction
3243 step makes the problem smaller by at least one
3244 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3245 if you give the <option>-XUndecidableInstances</option>
3246 flag (<xref linkend="undecidable-instances"/>).
3247 You can find lots of background material about the reason for these
3248 restrictions in the paper <ulink
3249 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3250 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3253 For example, these are OK:
3255 instance C Int [a] -- Multiple parameters
3256 instance Eq (S [a]) -- Structured type in head
3258 -- Repeated type variable in head
3259 instance C4 a a => C4 [a] [a]
3260 instance Stateful (ST s) (MutVar s)
3262 -- Head can consist of type variables only
3264 instance (Eq a, Show b) => C2 a b
3266 -- Non-type variables in context
3267 instance Show (s a) => Show (Sized s a)
3268 instance C2 Int a => C3 Bool [a]
3269 instance C2 Int a => C3 [a] b
3273 -- Context assertion no smaller than head
3274 instance C a => C a where ...
3275 -- (C b b) has more more occurrences of b than the head
3276 instance C b b => Foo [b] where ...
3281 The same restrictions apply to instances generated by
3282 <literal>deriving</literal> clauses. Thus the following is accepted:
3284 data MinHeap h a = H a (h a)
3287 because the derived instance
3289 instance (Show a, Show (h a)) => Show (MinHeap h a)
3291 conforms to the above rules.
3295 A useful idiom permitted by the above rules is as follows.
3296 If one allows overlapping instance declarations then it's quite
3297 convenient to have a "default instance" declaration that applies if
3298 something more specific does not:
3306 <sect3 id="undecidable-instances">
3307 <title>Undecidable instances</title>
3310 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3311 For example, sometimes you might want to use the following to get the
3312 effect of a "class synonym":
3314 class (C1 a, C2 a, C3 a) => C a where { }
3316 instance (C1 a, C2 a, C3 a) => C a where { }
3318 This allows you to write shorter signatures:
3324 f :: (C1 a, C2 a, C3 a) => ...
3326 The restrictions on functional dependencies (<xref
3327 linkend="functional-dependencies"/>) are particularly troublesome.
3328 It is tempting to introduce type variables in the context that do not appear in
3329 the head, something that is excluded by the normal rules. For example:
3331 class HasConverter a b | a -> b where
3334 data Foo a = MkFoo a
3336 instance (HasConverter a b,Show b) => Show (Foo a) where
3337 show (MkFoo value) = show (convert value)
3339 This is dangerous territory, however. Here, for example, is a program that would make the
3344 instance F [a] [[a]]
3345 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3347 Similarly, it can be tempting to lift the coverage condition:
3349 class Mul a b c | a b -> c where
3350 (.*.) :: a -> b -> c
3352 instance Mul Int Int Int where (.*.) = (*)
3353 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3354 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3356 The third instance declaration does not obey the coverage condition;
3357 and indeed the (somewhat strange) definition:
3359 f = \ b x y -> if b then x .*. [y] else y
3361 makes instance inference go into a loop, because it requires the constraint
3362 <literal>(Mul a [b] b)</literal>.
3365 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3366 the experimental flag <option>-XUndecidableInstances</option>
3367 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3368 both the Paterson Conditions and the Coverage Condition
3369 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3370 fixed-depth recursion stack. If you exceed the stack depth you get a
3371 sort of backtrace, and the opportunity to increase the stack depth
3372 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3378 <sect3 id="instance-overlap">
3379 <title>Overlapping instances</title>
3381 In general, <emphasis>GHC requires that that it be unambiguous which instance
3383 should be used to resolve a type-class constraint</emphasis>. This behaviour
3384 can be modified by two flags: <option>-XOverlappingInstances</option>
3385 <indexterm><primary>-XOverlappingInstances
3386 </primary></indexterm>
3387 and <option>-XIncoherentInstances</option>
3388 <indexterm><primary>-XIncoherentInstances
3389 </primary></indexterm>, as this section discusses. Both these
3390 flags are dynamic flags, and can be set on a per-module basis, using
3391 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3393 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3394 it tries to match every instance declaration against the
3396 by instantiating the head of the instance declaration. For example, consider
3399 instance context1 => C Int a where ... -- (A)
3400 instance context2 => C a Bool where ... -- (B)
3401 instance context3 => C Int [a] where ... -- (C)
3402 instance context4 => C Int [Int] where ... -- (D)
3404 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3405 but (C) and (D) do not. When matching, GHC takes
3406 no account of the context of the instance declaration
3407 (<literal>context1</literal> etc).
3408 GHC's default behaviour is that <emphasis>exactly one instance must match the
3409 constraint it is trying to resolve</emphasis>.
3410 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3411 including both declarations (A) and (B), say); an error is only reported if a
3412 particular constraint matches more than one.
3416 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3417 more than one instance to match, provided there is a most specific one. For
3418 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3419 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3420 most-specific match, the program is rejected.
3423 However, GHC is conservative about committing to an overlapping instance. For example:
3428 Suppose that from the RHS of <literal>f</literal> we get the constraint
3429 <literal>C Int [b]</literal>. But
3430 GHC does not commit to instance (C), because in a particular
3431 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3432 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3433 So GHC rejects the program.
3434 (If you add the flag <option>-XIncoherentInstances</option>,
3435 GHC will instead pick (C), without complaining about
3436 the problem of subsequent instantiations.)
3439 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3440 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3441 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3442 it instead. In this case, GHC will refrain from
3443 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3444 as before) but, rather than rejecting the program, it will infer the type
3446 f :: C Int [b] => [b] -> [b]
3448 That postpones the question of which instance to pick to the
3449 call site for <literal>f</literal>
3450 by which time more is known about the type <literal>b</literal>.
3451 You can write this type signature yourself if you use the
3452 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3456 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3460 instance Foo [b] where
3463 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3464 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3465 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3466 declaration. The solution is to postpone the choice by adding the constraint to the context
3467 of the instance declaration, thus:
3469 instance C Int [b] => Foo [b] where
3472 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3475 The willingness to be overlapped or incoherent is a property of
3476 the <emphasis>instance declaration</emphasis> itself, controlled by the
3477 presence or otherwise of the <option>-XOverlappingInstances</option>
3478 and <option>-XIncoherentInstances</option> flags when that module is
3479 being defined. Neither flag is required in a module that imports and uses the
3480 instance declaration. Specifically, during the lookup process:
3483 An instance declaration is ignored during the lookup process if (a) a more specific
3484 match is found, and (b) the instance declaration was compiled with
3485 <option>-XOverlappingInstances</option>. The flag setting for the
3486 more-specific instance does not matter.
3489 Suppose an instance declaration does not match the constraint being looked up, but
3490 does unify with it, so that it might match when the constraint is further
3491 instantiated. Usually GHC will regard this as a reason for not committing to
3492 some other constraint. But if the instance declaration was compiled with
3493 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3494 check for that declaration.
3497 These rules make it possible for a library author to design a library that relies on
3498 overlapping instances without the library client having to know.
3501 If an instance declaration is compiled without
3502 <option>-XOverlappingInstances</option>,
3503 then that instance can never be overlapped. This could perhaps be
3504 inconvenient. Perhaps the rule should instead say that the
3505 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3506 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3507 at a usage site should be permitted regardless of how the instance declarations
3508 are compiled, if the <option>-XOverlappingInstances</option> flag is
3509 used at the usage site. (Mind you, the exact usage site can occasionally be
3510 hard to pin down.) We are interested to receive feedback on these points.
3512 <para>The <option>-XIncoherentInstances</option> flag implies the
3513 <option>-XOverlappingInstances</option> flag, but not vice versa.
3518 <title>Type synonyms in the instance head</title>
3521 <emphasis>Unlike Haskell 98, instance heads may use type
3522 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3523 As always, using a type synonym is just shorthand for
3524 writing the RHS of the type synonym definition. For example:
3528 type Point = (Int,Int)
3529 instance C Point where ...
3530 instance C [Point] where ...
3534 is legal. However, if you added
3538 instance C (Int,Int) where ...
3542 as well, then the compiler will complain about the overlapping
3543 (actually, identical) instance declarations. As always, type synonyms
3544 must be fully applied. You cannot, for example, write:
3549 instance Monad P where ...
3553 This design decision is independent of all the others, and easily
3554 reversed, but it makes sense to me.
3562 <sect2 id="overloaded-strings">
3563 <title>Overloaded string literals
3567 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3568 string literal has type <literal>String</literal>, but with overloaded string
3569 literals enabled (with <literal>-XOverloadedStrings</literal>)
3570 a string literal has type <literal>(IsString a) => a</literal>.
3573 This means that the usual string syntax can be used, e.g., for packed strings
3574 and other variations of string like types. String literals behave very much
3575 like integer literals, i.e., they can be used in both expressions and patterns.
3576 If used in a pattern the literal with be replaced by an equality test, in the same
3577 way as an integer literal is.
3580 The class <literal>IsString</literal> is defined as:
3582 class IsString a where
3583 fromString :: String -> a
3585 The only predefined instance is the obvious one to make strings work as usual:
3587 instance IsString [Char] where
3590 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3591 it explicitly (for example, to give an instance declaration for it), you can import it
3592 from module <literal>GHC.Exts</literal>.
3595 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3599 Each type in a default declaration must be an
3600 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3604 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3605 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3606 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3607 <emphasis>or</emphasis> <literal>IsString</literal>.
3616 import GHC.Exts( IsString(..) )
3618 newtype MyString = MyString String deriving (Eq, Show)
3619 instance IsString MyString where
3620 fromString = MyString
3622 greet :: MyString -> MyString
3623 greet "hello" = "world"
3627 print $ greet "hello"
3628 print $ greet "fool"
3632 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3633 to work since it gets translated into an equality comparison.
3639 <sect1 id="other-type-extensions">
3640 <title>Other type system extensions</title>
3642 <sect2 id="type-restrictions">
3643 <title>Type signatures</title>
3645 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3647 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
3648 that the type-class constraints in a type signature must have the
3649 form <emphasis>(class type-variable)</emphasis> or
3650 <emphasis>(class (type-variable type-variable ...))</emphasis>.
3651 With <option>-XFlexibleContexts</option>
3652 these type signatures are perfectly OK
3655 g :: Ord (T a ()) => ...
3659 GHC imposes the following restrictions on the constraints in a type signature.
3663 forall tv1..tvn (c1, ...,cn) => type
3666 (Here, we write the "foralls" explicitly, although the Haskell source
3667 language omits them; in Haskell 98, all the free type variables of an
3668 explicit source-language type signature are universally quantified,
3669 except for the class type variables in a class declaration. However,
3670 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3679 <emphasis>Each universally quantified type variable
3680 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3682 A type variable <literal>a</literal> is "reachable" if it appears
3683 in the same constraint as either a type variable free in
3684 <literal>type</literal>, or another reachable type variable.
3685 A value with a type that does not obey
3686 this reachability restriction cannot be used without introducing
3687 ambiguity; that is why the type is rejected.
3688 Here, for example, is an illegal type:
3692 forall a. Eq a => Int
3696 When a value with this type was used, the constraint <literal>Eq tv</literal>
3697 would be introduced where <literal>tv</literal> is a fresh type variable, and
3698 (in the dictionary-translation implementation) the value would be
3699 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3700 can never know which instance of <literal>Eq</literal> to use because we never
3701 get any more information about <literal>tv</literal>.
3705 that the reachability condition is weaker than saying that <literal>a</literal> is
3706 functionally dependent on a type variable free in
3707 <literal>type</literal> (see <xref
3708 linkend="functional-dependencies"/>). The reason for this is there
3709 might be a "hidden" dependency, in a superclass perhaps. So
3710 "reachable" is a conservative approximation to "functionally dependent".
3711 For example, consider:
3713 class C a b | a -> b where ...
3714 class C a b => D a b where ...
3715 f :: forall a b. D a b => a -> a
3717 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3718 but that is not immediately apparent from <literal>f</literal>'s type.
3724 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3725 universally quantified type variables <literal>tvi</literal></emphasis>.
3727 For example, this type is OK because <literal>C a b</literal> mentions the
3728 universally quantified type variable <literal>b</literal>:
3732 forall a. C a b => burble
3736 The next type is illegal because the constraint <literal>Eq b</literal> does not
3737 mention <literal>a</literal>:
3741 forall a. Eq b => burble
3745 The reason for this restriction is milder than the other one. The
3746 excluded types are never useful or necessary (because the offending
3747 context doesn't need to be witnessed at this point; it can be floated
3748 out). Furthermore, floating them out increases sharing. Lastly,
3749 excluding them is a conservative choice; it leaves a patch of
3750 territory free in case we need it later.
3764 <sect2 id="implicit-parameters">
3765 <title>Implicit parameters</title>
3767 <para> Implicit parameters are implemented as described in
3768 "Implicit parameters: dynamic scoping with static types",
3769 J Lewis, MB Shields, E Meijer, J Launchbury,
3770 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3774 <para>(Most of the following, still rather incomplete, documentation is
3775 due to Jeff Lewis.)</para>
3777 <para>Implicit parameter support is enabled with the option
3778 <option>-XImplicitParams</option>.</para>
3781 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3782 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3783 context. In Haskell, all variables are statically bound. Dynamic
3784 binding of variables is a notion that goes back to Lisp, but was later
3785 discarded in more modern incarnations, such as Scheme. Dynamic binding
3786 can be very confusing in an untyped language, and unfortunately, typed
3787 languages, in particular Hindley-Milner typed languages like Haskell,
3788 only support static scoping of variables.
3791 However, by a simple extension to the type class system of Haskell, we
3792 can support dynamic binding. Basically, we express the use of a
3793 dynamically bound variable as a constraint on the type. These
3794 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3795 function uses a dynamically-bound variable <literal>?x</literal>
3796 of type <literal>t'</literal>". For
3797 example, the following expresses the type of a sort function,
3798 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3800 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3802 The dynamic binding constraints are just a new form of predicate in the type class system.
3805 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3806 where <literal>x</literal> is
3807 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3808 Use of this construct also introduces a new
3809 dynamic-binding constraint in the type of the expression.
3810 For example, the following definition
3811 shows how we can define an implicitly parameterized sort function in
3812 terms of an explicitly parameterized <literal>sortBy</literal> function:
3814 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3816 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3822 <title>Implicit-parameter type constraints</title>
3824 Dynamic binding constraints behave just like other type class
3825 constraints in that they are automatically propagated. Thus, when a
3826 function is used, its implicit parameters are inherited by the
3827 function that called it. For example, our <literal>sort</literal> function might be used
3828 to pick out the least value in a list:
3830 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3831 least xs = head (sort xs)
3833 Without lifting a finger, the <literal>?cmp</literal> parameter is
3834 propagated to become a parameter of <literal>least</literal> as well. With explicit
3835 parameters, the default is that parameters must always be explicit
3836 propagated. With implicit parameters, the default is to always
3840 An implicit-parameter type constraint differs from other type class constraints in the
3841 following way: All uses of a particular implicit parameter must have
3842 the same type. This means that the type of <literal>(?x, ?x)</literal>
3843 is <literal>(?x::a) => (a,a)</literal>, and not
3844 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3848 <para> You can't have an implicit parameter in the context of a class or instance
3849 declaration. For example, both these declarations are illegal:
3851 class (?x::Int) => C a where ...
3852 instance (?x::a) => Foo [a] where ...
3854 Reason: exactly which implicit parameter you pick up depends on exactly where
3855 you invoke a function. But the ``invocation'' of instance declarations is done
3856 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3857 Easiest thing is to outlaw the offending types.</para>
3859 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3861 f :: (?x :: [a]) => Int -> Int
3864 g :: (Read a, Show a) => String -> String
3867 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3868 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3869 quite unambiguous, and fixes the type <literal>a</literal>.
3874 <title>Implicit-parameter bindings</title>
3877 An implicit parameter is <emphasis>bound</emphasis> using the standard
3878 <literal>let</literal> or <literal>where</literal> binding forms.
3879 For example, we define the <literal>min</literal> function by binding
3880 <literal>cmp</literal>.
3883 min = let ?cmp = (<=) in least
3887 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3888 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3889 (including in a list comprehension, or do-notation, or pattern guards),
3890 or a <literal>where</literal> clause.
3891 Note the following points:
3894 An implicit-parameter binding group must be a
3895 collection of simple bindings to implicit-style variables (no
3896 function-style bindings, and no type signatures); these bindings are
3897 neither polymorphic or recursive.
3900 You may not mix implicit-parameter bindings with ordinary bindings in a
3901 single <literal>let</literal>
3902 expression; use two nested <literal>let</literal>s instead.
3903 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3907 You may put multiple implicit-parameter bindings in a
3908 single binding group; but they are <emphasis>not</emphasis> treated
3909 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3910 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3911 parameter. The bindings are not nested, and may be re-ordered without changing
3912 the meaning of the program.
3913 For example, consider:
3915 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3917 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3918 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3920 f :: (?x::Int) => Int -> Int
3928 <sect3><title>Implicit parameters and polymorphic recursion</title>
3931 Consider these two definitions:
3934 len1 xs = let ?acc = 0 in len_acc1 xs
3937 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3942 len2 xs = let ?acc = 0 in len_acc2 xs
3944 len_acc2 :: (?acc :: Int) => [a] -> Int
3946 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3948 The only difference between the two groups is that in the second group
3949 <literal>len_acc</literal> is given a type signature.
3950 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3951 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3952 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3953 has a type signature, the recursive call is made to the
3954 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3955 as an implicit parameter. So we get the following results in GHCi:
3962 Adding a type signature dramatically changes the result! This is a rather
3963 counter-intuitive phenomenon, worth watching out for.
3967 <sect3><title>Implicit parameters and monomorphism</title>
3969 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3970 Haskell Report) to implicit parameters. For example, consider:
3978 Since the binding for <literal>y</literal> falls under the Monomorphism
3979 Restriction it is not generalised, so the type of <literal>y</literal> is
3980 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3981 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3982 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3983 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3984 <literal>y</literal> in the body of the <literal>let</literal> will see the
3985 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3986 <literal>14</literal>.
3991 <!-- ======================= COMMENTED OUT ========================
3993 We intend to remove linear implicit parameters, so I'm at least removing
3994 them from the 6.6 user manual
3996 <sect2 id="linear-implicit-parameters">
3997 <title>Linear implicit parameters</title>
3999 Linear implicit parameters are an idea developed by Koen Claessen,
4000 Mark Shields, and Simon PJ. They address the long-standing
4001 problem that monads seem over-kill for certain sorts of problem, notably:
4004 <listitem> <para> distributing a supply of unique names </para> </listitem>
4005 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4006 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4010 Linear implicit parameters are just like ordinary implicit parameters,
4011 except that they are "linear"; that is, they cannot be copied, and
4012 must be explicitly "split" instead. Linear implicit parameters are
4013 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4014 (The '/' in the '%' suggests the split!)
4019 import GHC.Exts( Splittable )
4021 data NameSupply = ...
4023 splitNS :: NameSupply -> (NameSupply, NameSupply)
4024 newName :: NameSupply -> Name
4026 instance Splittable NameSupply where
4030 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4031 f env (Lam x e) = Lam x' (f env e)
4034 env' = extend env x x'
4035 ...more equations for f...
4037 Notice that the implicit parameter %ns is consumed
4039 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4040 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4044 So the translation done by the type checker makes
4045 the parameter explicit:
4047 f :: NameSupply -> Env -> Expr -> Expr
4048 f ns env (Lam x e) = Lam x' (f ns1 env e)
4050 (ns1,ns2) = splitNS ns
4052 env = extend env x x'
4054 Notice the call to 'split' introduced by the type checker.
4055 How did it know to use 'splitNS'? Because what it really did
4056 was to introduce a call to the overloaded function 'split',
4057 defined by the class <literal>Splittable</literal>:
4059 class Splittable a where
4062 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4063 split for name supplies. But we can simply write
4069 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4071 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4072 <literal>GHC.Exts</literal>.
4077 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4078 are entirely distinct implicit parameters: you
4079 can use them together and they won't interfere with each other. </para>
4082 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4084 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4085 in the context of a class or instance declaration. </para></listitem>
4089 <sect3><title>Warnings</title>
4092 The monomorphism restriction is even more important than usual.
4093 Consider the example above:
4095 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4096 f env (Lam x e) = Lam x' (f env e)
4099 env' = extend env x x'
4101 If we replaced the two occurrences of x' by (newName %ns), which is
4102 usually a harmless thing to do, we get:
4104 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4105 f env (Lam x e) = Lam (newName %ns) (f env e)
4107 env' = extend env x (newName %ns)
4109 But now the name supply is consumed in <emphasis>three</emphasis> places
4110 (the two calls to newName,and the recursive call to f), so
4111 the result is utterly different. Urk! We don't even have
4115 Well, this is an experimental change. With implicit
4116 parameters we have already lost beta reduction anyway, and
4117 (as John Launchbury puts it) we can't sensibly reason about
4118 Haskell programs without knowing their typing.
4123 <sect3><title>Recursive functions</title>
4124 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4127 foo :: %x::T => Int -> [Int]
4129 foo n = %x : foo (n-1)
4131 where T is some type in class Splittable.</para>
4133 Do you get a list of all the same T's or all different T's
4134 (assuming that split gives two distinct T's back)?
4136 If you supply the type signature, taking advantage of polymorphic
4137 recursion, you get what you'd probably expect. Here's the
4138 translated term, where the implicit param is made explicit:
4141 foo x n = let (x1,x2) = split x
4142 in x1 : foo x2 (n-1)
4144 But if you don't supply a type signature, GHC uses the Hindley
4145 Milner trick of using a single monomorphic instance of the function
4146 for the recursive calls. That is what makes Hindley Milner type inference
4147 work. So the translation becomes
4151 foom n = x : foom (n-1)
4155 Result: 'x' is not split, and you get a list of identical T's. So the
4156 semantics of the program depends on whether or not foo has a type signature.
4159 You may say that this is a good reason to dislike linear implicit parameters
4160 and you'd be right. That is why they are an experimental feature.
4166 ================ END OF Linear Implicit Parameters commented out -->
4168 <sect2 id="kinding">
4169 <title>Explicitly-kinded quantification</title>
4172 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4173 to give the kind explicitly as (machine-checked) documentation,
4174 just as it is nice to give a type signature for a function. On some occasions,
4175 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4176 John Hughes had to define the data type:
4178 data Set cxt a = Set [a]
4179 | Unused (cxt a -> ())
4181 The only use for the <literal>Unused</literal> constructor was to force the correct
4182 kind for the type variable <literal>cxt</literal>.
4185 GHC now instead allows you to specify the kind of a type variable directly, wherever
4186 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4189 This flag enables kind signatures in the following places:
4191 <listitem><para><literal>data</literal> declarations:
4193 data Set (cxt :: * -> *) a = Set [a]
4194 </screen></para></listitem>
4195 <listitem><para><literal>type</literal> declarations:
4197 type T (f :: * -> *) = f Int
4198 </screen></para></listitem>
4199 <listitem><para><literal>class</literal> declarations:
4201 class (Eq a) => C (f :: * -> *) a where ...
4202 </screen></para></listitem>
4203 <listitem><para><literal>forall</literal>'s in type signatures:
4205 f :: forall (cxt :: * -> *). Set cxt Int
4206 </screen></para></listitem>
4211 The parentheses are required. Some of the spaces are required too, to
4212 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4213 will get a parse error, because "<literal>::*->*</literal>" is a
4214 single lexeme in Haskell.
4218 As part of the same extension, you can put kind annotations in types
4221 f :: (Int :: *) -> Int
4222 g :: forall a. a -> (a :: *)
4226 atype ::= '(' ctype '::' kind ')
4228 The parentheses are required.
4233 <sect2 id="universal-quantification">
4234 <title>Arbitrary-rank polymorphism
4238 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4239 allows us to say exactly what this means. For example:
4247 g :: forall b. (b -> b)
4249 The two are treated identically.
4253 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4254 explicit universal quantification in
4256 For example, all the following types are legal:
4258 f1 :: forall a b. a -> b -> a
4259 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4261 f2 :: (forall a. a->a) -> Int -> Int
4262 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4264 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4266 f4 :: Int -> (forall a. a -> a)
4268 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4269 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4270 The <literal>forall</literal> makes explicit the universal quantification that
4271 is implicitly added by Haskell.
4274 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4275 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4276 shows, the polymorphic type on the left of the function arrow can be overloaded.
4279 The function <literal>f3</literal> has a rank-3 type;
4280 it has rank-2 types on the left of a function arrow.
4283 GHC has three flags to control higher-rank types:
4286 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4289 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4292 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4293 That is, you can nest <literal>forall</literal>s
4294 arbitrarily deep in function arrows.
4295 In particular, a forall-type (also called a "type scheme"),
4296 including an operational type class context, is legal:
4298 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4299 of a function arrow </para> </listitem>
4300 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4301 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4302 field type signatures.</para> </listitem>
4303 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4304 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4308 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4309 a type variable any more!
4318 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4319 the types of the constructor arguments. Here are several examples:
4325 data T a = T1 (forall b. b -> b -> b) a
4327 data MonadT m = MkMonad { return :: forall a. a -> m a,
4328 bind :: forall a b. m a -> (a -> m b) -> m b
4331 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4337 The constructors have rank-2 types:
4343 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4344 MkMonad :: forall m. (forall a. a -> m a)
4345 -> (forall a b. m a -> (a -> m b) -> m b)
4347 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4353 Notice that you don't need to use a <literal>forall</literal> if there's an
4354 explicit context. For example in the first argument of the
4355 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4356 prefixed to the argument type. The implicit <literal>forall</literal>
4357 quantifies all type variables that are not already in scope, and are
4358 mentioned in the type quantified over.
4362 As for type signatures, implicit quantification happens for non-overloaded
4363 types too. So if you write this:
4366 data T a = MkT (Either a b) (b -> b)
4369 it's just as if you had written this:
4372 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4375 That is, since the type variable <literal>b</literal> isn't in scope, it's
4376 implicitly universally quantified. (Arguably, it would be better
4377 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4378 where that is what is wanted. Feedback welcomed.)
4382 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4383 the constructor to suitable values, just as usual. For example,
4394 a3 = MkSwizzle reverse
4397 a4 = let r x = Just x
4404 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4405 mkTs f x y = [T1 f x, T1 f y]
4411 The type of the argument can, as usual, be more general than the type
4412 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4413 does not need the <literal>Ord</literal> constraint.)
4417 When you use pattern matching, the bound variables may now have
4418 polymorphic types. For example:
4424 f :: T a -> a -> (a, Char)
4425 f (T1 w k) x = (w k x, w 'c' 'd')
4427 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4428 g (MkSwizzle s) xs f = s (map f (s xs))
4430 h :: MonadT m -> [m a] -> m [a]
4431 h m [] = return m []
4432 h m (x:xs) = bind m x $ \y ->
4433 bind m (h m xs) $ \ys ->
4440 In the function <function>h</function> we use the record selectors <literal>return</literal>
4441 and <literal>bind</literal> to extract the polymorphic bind and return functions
4442 from the <literal>MonadT</literal> data structure, rather than using pattern
4448 <title>Type inference</title>
4451 In general, type inference for arbitrary-rank types is undecidable.
4452 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4453 to get a decidable algorithm by requiring some help from the programmer.
4454 We do not yet have a formal specification of "some help" but the rule is this:
4457 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4458 provides an explicit polymorphic type for x, or GHC's type inference will assume
4459 that x's type has no foralls in it</emphasis>.
4462 What does it mean to "provide" an explicit type for x? You can do that by
4463 giving a type signature for x directly, using a pattern type signature
4464 (<xref linkend="scoped-type-variables"/>), thus:
4466 \ f :: (forall a. a->a) -> (f True, f 'c')
4468 Alternatively, you can give a type signature to the enclosing
4469 context, which GHC can "push down" to find the type for the variable:
4471 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4473 Here the type signature on the expression can be pushed inwards
4474 to give a type signature for f. Similarly, and more commonly,
4475 one can give a type signature for the function itself:
4477 h :: (forall a. a->a) -> (Bool,Char)
4478 h f = (f True, f 'c')
4480 You don't need to give a type signature if the lambda bound variable
4481 is a constructor argument. Here is an example we saw earlier:
4483 f :: T a -> a -> (a, Char)
4484 f (T1 w k) x = (w k x, w 'c' 'd')
4486 Here we do not need to give a type signature to <literal>w</literal>, because
4487 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4494 <sect3 id="implicit-quant">
4495 <title>Implicit quantification</title>
4498 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4499 user-written types, if and only if there is no explicit <literal>forall</literal>,
4500 GHC finds all the type variables mentioned in the type that are not already
4501 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4505 f :: forall a. a -> a
4512 h :: forall b. a -> b -> b
4518 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4521 f :: (a -> a) -> Int
4523 f :: forall a. (a -> a) -> Int
4525 f :: (forall a. a -> a) -> Int
4528 g :: (Ord a => a -> a) -> Int
4529 -- MEANS the illegal type
4530 g :: forall a. (Ord a => a -> a) -> Int
4532 g :: (forall a. Ord a => a -> a) -> Int
4534 The latter produces an illegal type, which you might think is silly,
4535 but at least the rule is simple. If you want the latter type, you
4536 can write your for-alls explicitly. Indeed, doing so is strongly advised
4543 <sect2 id="impredicative-polymorphism">
4544 <title>Impredicative polymorphism
4546 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4547 enabled with <option>-XImpredicativeTypes</option>.
4549 that you can call a polymorphic function at a polymorphic type, and
4550 parameterise data structures over polymorphic types. For example:
4552 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4553 f (Just g) = Just (g [3], g "hello")
4556 Notice here that the <literal>Maybe</literal> type is parameterised by the
4557 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4560 <para>The technical details of this extension are described in the paper
4561 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4562 type inference for higher-rank types and impredicativity</ulink>,
4563 which appeared at ICFP 2006.
4567 <sect2 id="scoped-type-variables">
4568 <title>Lexically scoped type variables
4572 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4573 which some type signatures are simply impossible to write. For example:
4575 f :: forall a. [a] -> [a]
4581 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4582 the entire definition of <literal>f</literal>.
4583 In particular, it is in scope at the type signature for <varname>ys</varname>.
4584 In Haskell 98 it is not possible to declare
4585 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4586 it becomes possible to do so.
4588 <para>Lexically-scoped type variables are enabled by
4589 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4591 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4592 variables work, compared to earlier releases. Read this section
4596 <title>Overview</title>
4598 <para>The design follows the following principles
4600 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4601 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4602 design.)</para></listitem>
4603 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4604 type variables. This means that every programmer-written type signature
4605 (including one that contains free scoped type variables) denotes a
4606 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4607 checker, and no inference is involved.</para></listitem>
4608 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4609 changing the program.</para></listitem>
4613 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4615 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4616 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4617 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4618 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4622 In Haskell, a programmer-written type signature is implicitly quantified over
4623 its free type variables (<ulink
4624 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4626 of the Haskell Report).
4627 Lexically scoped type variables affect this implicit quantification rules
4628 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4629 quantified. For example, if type variable <literal>a</literal> is in scope,
4632 (e :: a -> a) means (e :: a -> a)
4633 (e :: b -> b) means (e :: forall b. b->b)
4634 (e :: a -> b) means (e :: forall b. a->b)
4642 <sect3 id="decl-type-sigs">
4643 <title>Declaration type signatures</title>
4644 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4645 quantification (using <literal>forall</literal>) brings into scope the
4646 explicitly-quantified
4647 type variables, in the definition of the named function. For example:
4649 f :: forall a. [a] -> [a]
4650 f (x:xs) = xs ++ [ x :: a ]
4652 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4653 the definition of "<literal>f</literal>".
4655 <para>This only happens if:
4657 <listitem><para> The quantification in <literal>f</literal>'s type
4658 signature is explicit. For example:
4661 g (x:xs) = xs ++ [ x :: a ]
4663 This program will be rejected, because "<literal>a</literal>" does not scope
4664 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4665 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4666 quantification rules.
4668 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4669 not a pattern binding.
4672 f1 :: forall a. [a] -> [a]
4673 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4675 f2 :: forall a. [a] -> [a]
4676 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4678 f3 :: forall a. [a] -> [a]
4679 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4681 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4682 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4683 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4684 the type signature brings <literal>a</literal> into scope.
4690 <sect3 id="exp-type-sigs">
4691 <title>Expression type signatures</title>
4693 <para>An expression type signature that has <emphasis>explicit</emphasis>
4694 quantification (using <literal>forall</literal>) brings into scope the
4695 explicitly-quantified
4696 type variables, in the annotated expression. For example:
4698 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4700 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4701 type variable <literal>s</literal> into scope, in the annotated expression
4702 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4707 <sect3 id="pattern-type-sigs">
4708 <title>Pattern type signatures</title>
4710 A type signature may occur in any pattern; this is a <emphasis>pattern type
4711 signature</emphasis>.
4714 -- f and g assume that 'a' is already in scope
4715 f = \(x::Int, y::a) -> x
4717 h ((x,y) :: (Int,Bool)) = (y,x)
4719 In the case where all the type variables in the pattern type signature are
4720 already in scope (i.e. bound by the enclosing context), matters are simple: the
4721 signature simply constrains the type of the pattern in the obvious way.
4724 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4725 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4726 that are already in scope. For example:
4728 f :: forall a. [a] -> (Int, [a])
4731 (ys::[a], n) = (reverse xs, length xs) -- OK
4732 zs::[a] = xs ++ ys -- OK
4734 Just (v::b) = ... -- Not OK; b is not in scope
4736 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4737 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4741 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4742 type signature may mention a type variable that is not in scope; in this case,
4743 <emphasis>the signature brings that type variable into scope</emphasis>.
4744 This is particularly important for existential data constructors. For example:
4746 data T = forall a. MkT [a]
4749 k (MkT [t::a]) = MkT t3
4753 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4754 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4755 because it is bound by the pattern match. GHC's rule is that in this situation
4756 (and only then), a pattern type signature can mention a type variable that is
4757 not already in scope; the effect is to bring it into scope, standing for the
4758 existentially-bound type variable.
4761 When a pattern type signature binds a type variable in this way, GHC insists that the
4762 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4763 This means that any user-written type signature always stands for a completely known type.
4766 If all this seems a little odd, we think so too. But we must have
4767 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4768 could not name existentially-bound type variables in subsequent type signatures.
4771 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4772 signature is allowed to mention a lexical variable that is not already in
4774 For example, both <literal>f</literal> and <literal>g</literal> would be
4775 illegal if <literal>a</literal> was not already in scope.
4781 <!-- ==================== Commented out part about result type signatures
4783 <sect3 id="result-type-sigs">
4784 <title>Result type signatures</title>
4787 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4790 {- f assumes that 'a' is already in scope -}
4791 f x y :: [a] = [x,y,x]
4793 g = \ x :: [Int] -> [3,4]
4795 h :: forall a. [a] -> a
4799 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4800 the result of the function. Similarly, the body of the lambda in the RHS of
4801 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4802 alternative in <literal>h</literal> is <literal>a</literal>.
4804 <para> A result type signature never brings new type variables into scope.</para>
4806 There are a couple of syntactic wrinkles. First, notice that all three
4807 examples would parse quite differently with parentheses:
4809 {- f assumes that 'a' is already in scope -}
4810 f x (y :: [a]) = [x,y,x]
4812 g = \ (x :: [Int]) -> [3,4]
4814 h :: forall a. [a] -> a
4818 Now the signature is on the <emphasis>pattern</emphasis>; and
4819 <literal>h</literal> would certainly be ill-typed (since the pattern
4820 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4822 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4823 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4824 token or a parenthesised type of some sort). To see why,
4825 consider how one would parse this:
4834 <sect3 id="cls-inst-scoped-tyvars">
4835 <title>Class and instance declarations</title>
4838 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4839 scope over the methods defined in the <literal>where</literal> part. For example:
4857 <sect2 id="typing-binds">
4858 <title>Generalised typing of mutually recursive bindings</title>
4861 The Haskell Report specifies that a group of bindings (at top level, or in a
4862 <literal>let</literal> or <literal>where</literal>) should be sorted into
4863 strongly-connected components, and then type-checked in dependency order
4864 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4865 Report, Section 4.5.1</ulink>).
4866 As each group is type-checked, any binders of the group that
4868 an explicit type signature are put in the type environment with the specified
4870 and all others are monomorphic until the group is generalised
4871 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4874 <para>Following a suggestion of Mark Jones, in his paper
4875 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4877 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4879 <emphasis>the dependency analysis ignores references to variables that have an explicit
4880 type signature</emphasis>.
4881 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4882 typecheck. For example, consider:
4884 f :: Eq a => a -> Bool
4885 f x = (x == x) || g True || g "Yes"
4887 g y = (y <= y) || f True
4889 This is rejected by Haskell 98, but under Jones's scheme the definition for
4890 <literal>g</literal> is typechecked first, separately from that for
4891 <literal>f</literal>,
4892 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4893 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4894 type is generalised, to get
4896 g :: Ord a => a -> Bool
4898 Now, the definition for <literal>f</literal> is typechecked, with this type for
4899 <literal>g</literal> in the type environment.
4903 The same refined dependency analysis also allows the type signatures of
4904 mutually-recursive functions to have different contexts, something that is illegal in
4905 Haskell 98 (Section 4.5.2, last sentence). With
4906 <option>-XRelaxedPolyRec</option>
4907 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4908 type signatures; in practice this means that only variables bound by the same
4909 pattern binding must have the same context. For example, this is fine:
4911 f :: Eq a => a -> Bool
4912 f x = (x == x) || g True
4914 g :: Ord a => a -> Bool
4915 g y = (y <= y) || f True
4920 <sect2 id="type-families">
4921 <title>Type families
4925 GHC supports the definition of type families indexed by types. They may be
4926 seen as an extension of Haskell 98's class-based overloading of values to
4927 types. When type families are declared in classes, they are also known as
4931 There are two forms of type families: data families and type synonym families.
4932 Currently, only the former are fully implemented, while we are still working
4933 on the latter. As a result, the specification of the language extension is
4934 also still to some degree in flux. Hence, a more detailed description of
4935 the language extension and its use is currently available
4936 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4937 wiki page on type families</ulink>. The material will be moved to this user's
4938 guide when it has stabilised.
4941 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4948 <!-- ==================== End of type system extensions ================= -->
4950 <!-- ====================== TEMPLATE HASKELL ======================= -->
4952 <sect1 id="template-haskell">
4953 <title>Template Haskell</title>
4955 <para>Template Haskell allows you to do compile-time meta-programming in
4958 the main technical innovations is discussed in "<ulink
4959 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
4960 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4963 There is a Wiki page about
4964 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
4965 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4969 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4970 Haskell library reference material</ulink>
4971 (look for module <literal>Language.Haskell.TH</literal>).
4972 Many changes to the original design are described in
4973 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4974 Notes on Template Haskell version 2</ulink>.
4975 Not all of these changes are in GHC, however.
4978 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4979 as a worked example to help get you started.
4983 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4984 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4989 <title>Syntax</title>
4991 <para> Template Haskell has the following new syntactic
4992 constructions. You need to use the flag
4993 <option>-XTemplateHaskell</option>
4994 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4995 </indexterm>to switch these syntactic extensions on
4996 (<option>-XTemplateHaskell</option> is no longer implied by
4997 <option>-fglasgow-exts</option>).</para>
5001 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5002 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5003 There must be no space between the "$" and the identifier or parenthesis. This use
5004 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5005 of "." as an infix operator. If you want the infix operator, put spaces around it.
5007 <para> A splice can occur in place of
5009 <listitem><para> an expression; the spliced expression must
5010 have type <literal>Q Exp</literal></para></listitem>
5011 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5014 Inside a splice you can can only call functions defined in imported modules,
5015 not functions defined elsewhere in the same module.</listitem>
5019 A expression quotation is written in Oxford brackets, thus:
5021 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5022 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5023 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5024 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5025 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5026 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5027 </itemizedlist></para></listitem>
5030 A quasi-quotation can appear in either a pattern context or an
5031 expression context and is also written in Oxford brackets:
5033 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5034 where the "..." is an arbitrary string; a full description of the
5035 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5036 </itemizedlist></para></listitem>
5039 A name can be quoted with either one or two prefix single quotes:
5041 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5042 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5043 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5045 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5046 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5049 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5050 may also be given as an argument to the <literal>reify</literal> function.
5056 (Compared to the original paper, there are many differences of detail.
5057 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5058 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5059 Type splices are not implemented, and neither are pattern splices or quotations.
5063 <sect2> <title> Using Template Haskell </title>
5067 The data types and monadic constructor functions for Template Haskell are in the library
5068 <literal>Language.Haskell.THSyntax</literal>.
5072 You can only run a function at compile time if it is imported from another module. That is,
5073 you can't define a function in a module, and call it from within a splice in the same module.
5074 (It would make sense to do so, but it's hard to implement.)
5078 You can only run a function at compile time if it is imported
5079 from another module <emphasis>that is not part of a mutually-recursive group of modules
5080 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5081 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5082 splice is to be run.</para>
5084 For example, when compiling module A,
5085 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5086 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5090 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5093 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5094 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5095 compiles and runs a program, and then looks at the result. So it's important that
5096 the program it compiles produces results whose representations are identical to
5097 those of the compiler itself.
5101 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5102 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5107 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5108 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5109 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5116 -- Import our template "pr"
5117 import Printf ( pr )
5119 -- The splice operator $ takes the Haskell source code
5120 -- generated at compile time by "pr" and splices it into
5121 -- the argument of "putStrLn".
5122 main = putStrLn ( $(pr "Hello") )
5128 -- Skeletal printf from the paper.
5129 -- It needs to be in a separate module to the one where
5130 -- you intend to use it.
5132 -- Import some Template Haskell syntax
5133 import Language.Haskell.TH
5135 -- Describe a format string
5136 data Format = D | S | L String
5138 -- Parse a format string. This is left largely to you
5139 -- as we are here interested in building our first ever
5140 -- Template Haskell program and not in building printf.
5141 parse :: String -> [Format]
5144 -- Generate Haskell source code from a parsed representation
5145 -- of the format string. This code will be spliced into
5146 -- the module which calls "pr", at compile time.
5147 gen :: [Format] -> Q Exp
5148 gen [D] = [| \n -> show n |]
5149 gen [S] = [| \s -> s |]
5150 gen [L s] = stringE s
5152 -- Here we generate the Haskell code for the splice
5153 -- from an input format string.
5154 pr :: String -> Q Exp
5155 pr s = gen (parse s)
5158 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5161 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5164 <para>Run "main.exe" and here is your output:</para>
5174 <title>Using Template Haskell with Profiling</title>
5175 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5177 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5178 interpreter to run the splice expressions. The bytecode interpreter
5179 runs the compiled expression on top of the same runtime on which GHC
5180 itself is running; this means that the compiled code referred to by
5181 the interpreted expression must be compatible with this runtime, and
5182 in particular this means that object code that is compiled for
5183 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5184 expression, because profiled object code is only compatible with the
5185 profiling version of the runtime.</para>
5187 <para>This causes difficulties if you have a multi-module program
5188 containing Template Haskell code and you need to compile it for
5189 profiling, because GHC cannot load the profiled object code and use it
5190 when executing the splices. Fortunately GHC provides a workaround.
5191 The basic idea is to compile the program twice:</para>
5195 <para>Compile the program or library first the normal way, without
5196 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5199 <para>Then compile it again with <option>-prof</option>, and
5200 additionally use <option>-osuf
5201 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5202 to name the object files differently (you can choose any suffix
5203 that isn't the normal object suffix here). GHC will automatically
5204 load the object files built in the first step when executing splice
5205 expressions. If you omit the <option>-osuf</option> flag when
5206 building with <option>-prof</option> and Template Haskell is used,
5207 GHC will emit an error message. </para>
5212 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5213 <para>Quasi-quotation allows patterns and expressions to be written using
5214 programmer-defined concrete syntax; the motivation behind the extension and
5215 several examples are documented in
5216 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5217 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5218 2007). The example below shows how to write a quasiquoter for a simple
5219 expression language.</para>
5222 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5223 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5224 functions for quoting expressions and patterns, respectively. The first argument
5225 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5226 context of the quasi-quotation statement determines which of the two parsers is
5227 called: if the quasi-quotation occurs in an expression context, the expression
5228 parser is called, and if it occurs in a pattern context, the pattern parser is
5232 Note that in the example we make use of an antiquoted
5233 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5234 (this syntax for anti-quotation was defined by the parser's
5235 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5236 integer value argument of the constructor <literal>IntExpr</literal> when
5237 pattern matching. Please see the referenced paper for further details regarding
5238 anti-quotation as well as the description of a technique that uses SYB to
5239 leverage a single parser of type <literal>String -> a</literal> to generate both
5240 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5241 pattern parser that returns a value of type <literal>Q Pat</literal>.
5244 <para>In general, a quasi-quote has the form
5245 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5246 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5247 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5248 can be arbitrary, and may contain newlines.
5251 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5252 the example, <literal>expr</literal> cannot be defined
5253 in <literal>Main.hs</literal> where it is used, but must be imported.
5264 main = do { print $ eval [$expr|1 + 2|]
5266 { [$expr|'int:n|] -> print n
5275 import qualified Language.Haskell.TH as TH
5276 import Language.Haskell.TH.Quasi
5278 data Expr = IntExpr Integer
5279 | AntiIntExpr String
5280 | BinopExpr BinOp Expr Expr
5282 deriving(Show, Typeable, Data)
5288 deriving(Show, Typeable, Data)
5290 eval :: Expr -> Integer
5291 eval (IntExpr n) = n
5292 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5299 expr = QuasiQuoter parseExprExp parseExprPat
5301 -- Parse an Expr, returning its representation as
5302 -- either a Q Exp or a Q Pat. See the referenced paper
5303 -- for how to use SYB to do this by writing a single
5304 -- parser of type String -> Expr instead of two
5305 -- separate parsers.
5307 parseExprExp :: String -> Q Exp
5310 parseExprPat :: String -> Q Pat
5314 <para>Now run the compiler:
5317 $ ghc --make -XQuasiQuotes Main.hs -o main
5320 <para>Run "main" and here is your output:</para>
5332 <!-- ===================== Arrow notation =================== -->
5334 <sect1 id="arrow-notation">
5335 <title>Arrow notation
5338 <para>Arrows are a generalization of monads introduced by John Hughes.
5339 For more details, see
5344 “Generalising Monads to Arrows”,
5345 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5346 pp67–111, May 2000.
5347 The paper that introduced arrows: a friendly introduction, motivated with
5348 programming examples.
5354 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5355 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5356 Introduced the notation described here.
5362 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5363 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5370 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
5371 John Hughes, in <citetitle>5th International Summer School on
5372 Advanced Functional Programming</citetitle>,
5373 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
5375 This paper includes another introduction to the notation,
5376 with practical examples.
5382 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
5383 Ross Paterson and Simon Peyton Jones, September 16, 2004.
5384 A terse enumeration of the formal rules used
5385 (extracted from comments in the source code).
5391 The arrows web page at
5392 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5397 With the <option>-XArrows</option> flag, GHC supports the arrow
5398 notation described in the second of these papers,
5399 translating it using combinators from the
5400 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5402 What follows is a brief introduction to the notation;
5403 it won't make much sense unless you've read Hughes's paper.
5406 <para>The extension adds a new kind of expression for defining arrows:
5408 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5409 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5411 where <literal>proc</literal> is a new keyword.
5412 The variables of the pattern are bound in the body of the
5413 <literal>proc</literal>-expression,
5414 which is a new sort of thing called a <firstterm>command</firstterm>.
5415 The syntax of commands is as follows:
5417 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5418 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5419 | <replaceable>cmd</replaceable><superscript>0</superscript>
5421 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5422 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5423 infix operators as for expressions, and
5425 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5426 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5427 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5428 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5429 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5430 | <replaceable>fcmd</replaceable>
5432 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5433 | ( <replaceable>cmd</replaceable> )
5434 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5436 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5437 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5438 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5439 | <replaceable>cmd</replaceable>
5441 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5442 except that the bodies are commands instead of expressions.
5446 Commands produce values, but (like monadic computations)
5447 may yield more than one value,
5448 or none, and may do other things as well.
5449 For the most part, familiarity with monadic notation is a good guide to
5451 However the values of expressions, even monadic ones,
5452 are determined by the values of the variables they contain;
5453 this is not necessarily the case for commands.
5457 A simple example of the new notation is the expression
5459 proc x -> f -< x+1
5461 We call this a <firstterm>procedure</firstterm> or
5462 <firstterm>arrow abstraction</firstterm>.
5463 As with a lambda expression, the variable <literal>x</literal>
5464 is a new variable bound within the <literal>proc</literal>-expression.
5465 It refers to the input to the arrow.
5466 In the above example, <literal>-<</literal> is not an identifier but an
5467 new reserved symbol used for building commands from an expression of arrow
5468 type and an expression to be fed as input to that arrow.
5469 (The weird look will make more sense later.)
5470 It may be read as analogue of application for arrows.
5471 The above example is equivalent to the Haskell expression
5473 arr (\ x -> x+1) >>> f
5475 That would make no sense if the expression to the left of
5476 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5477 More generally, the expression to the left of <literal>-<</literal>
5478 may not involve any <firstterm>local variable</firstterm>,
5479 i.e. a variable bound in the current arrow abstraction.
5480 For such a situation there is a variant <literal>-<<</literal>, as in
5482 proc x -> f x -<< x+1
5484 which is equivalent to
5486 arr (\ x -> (f x, x+1)) >>> app
5488 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5490 Such an arrow is equivalent to a monad, so if you're using this form
5491 you may find a monadic formulation more convenient.
5495 <title>do-notation for commands</title>
5498 Another form of command is a form of <literal>do</literal>-notation.
5499 For example, you can write
5508 You can read this much like ordinary <literal>do</literal>-notation,
5509 but with commands in place of monadic expressions.
5510 The first line sends the value of <literal>x+1</literal> as an input to
5511 the arrow <literal>f</literal>, and matches its output against
5512 <literal>y</literal>.
5513 In the next line, the output is discarded.
5514 The arrow <function>returnA</function> is defined in the
5515 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5516 module as <literal>arr id</literal>.
5517 The above example is treated as an abbreviation for
5519 arr (\ x -> (x, x)) >>>
5520 first (arr (\ x -> x+1) >>> f) >>>
5521 arr (\ (y, x) -> (y, (x, y))) >>>
5522 first (arr (\ y -> 2*y) >>> g) >>>
5524 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5525 first (arr (\ (x, z) -> x*z) >>> h) >>>
5526 arr (\ (t, z) -> t+z) >>>
5529 Note that variables not used later in the composition are projected out.
5530 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5532 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5533 module, this reduces to
5535 arr (\ x -> (x+1, x)) >>>
5537 arr (\ (y, x) -> (2*y, (x, y))) >>>
5539 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5541 arr (\ (t, z) -> t+z)
5543 which is what you might have written by hand.
5544 With arrow notation, GHC keeps track of all those tuples of variables for you.
5548 Note that although the above translation suggests that
5549 <literal>let</literal>-bound variables like <literal>z</literal> must be
5550 monomorphic, the actual translation produces Core,
5551 so polymorphic variables are allowed.
5555 It's also possible to have mutually recursive bindings,
5556 using the new <literal>rec</literal> keyword, as in the following example:
5558 counter :: ArrowCircuit a => a Bool Int
5559 counter = proc reset -> do
5560 rec output <- returnA -< if reset then 0 else next
5561 next <- delay 0 -< output+1
5562 returnA -< output
5564 The translation of such forms uses the <function>loop</function> combinator,
5565 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5571 <title>Conditional commands</title>
5574 In the previous example, we used a conditional expression to construct the
5576 Sometimes we want to conditionally execute different commands, as in
5583 which is translated to
5585 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5586 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5588 Since the translation uses <function>|||</function>,
5589 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5593 There are also <literal>case</literal> commands, like
5599 y <- h -< (x1, x2)
5603 The syntax is the same as for <literal>case</literal> expressions,
5604 except that the bodies of the alternatives are commands rather than expressions.
5605 The translation is similar to that of <literal>if</literal> commands.
5611 <title>Defining your own control structures</title>
5614 As we're seen, arrow notation provides constructs,
5615 modelled on those for expressions,
5616 for sequencing, value recursion and conditionals.
5617 But suitable combinators,
5618 which you can define in ordinary Haskell,
5619 may also be used to build new commands out of existing ones.
5620 The basic idea is that a command defines an arrow from environments to values.
5621 These environments assign values to the free local variables of the command.
5622 Thus combinators that produce arrows from arrows
5623 may also be used to build commands from commands.
5624 For example, the <literal>ArrowChoice</literal> class includes a combinator
5626 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5628 so we can use it to build commands:
5630 expr' = proc x -> do
5633 symbol Plus -< ()
5634 y <- term -< ()
5637 symbol Minus -< ()
5638 y <- term -< ()
5641 (The <literal>do</literal> on the first line is needed to prevent the first
5642 <literal><+> ...</literal> from being interpreted as part of the
5643 expression on the previous line.)
5644 This is equivalent to
5646 expr' = (proc x -> returnA -< x)
5647 <+> (proc x -> do
5648 symbol Plus -< ()
5649 y <- term -< ()
5651 <+> (proc x -> do
5652 symbol Minus -< ()
5653 y <- term -< ()
5656 It is essential that this operator be polymorphic in <literal>e</literal>
5657 (representing the environment input to the command
5658 and thence to its subcommands)
5659 and satisfy the corresponding naturality property
5661 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5663 at least for strict <literal>k</literal>.
5664 (This should be automatic if you're not using <function>seq</function>.)
5665 This ensures that environments seen by the subcommands are environments
5666 of the whole command,
5667 and also allows the translation to safely trim these environments.
5668 The operator must also not use any variable defined within the current
5673 We could define our own operator
5675 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5676 untilA body cond = proc x ->
5677 b <- cond -< x
5678 if b then returnA -< ()
5681 untilA body cond -< x
5683 and use it in the same way.
5684 Of course this infix syntax only makes sense for binary operators;
5685 there is also a more general syntax involving special brackets:
5689 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5696 <title>Primitive constructs</title>
5699 Some operators will need to pass additional inputs to their subcommands.
5700 For example, in an arrow type supporting exceptions,
5701 the operator that attaches an exception handler will wish to pass the
5702 exception that occurred to the handler.
5703 Such an operator might have a type
5705 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5707 where <literal>Ex</literal> is the type of exceptions handled.
5708 You could then use this with arrow notation by writing a command
5710 body `handleA` \ ex -> handler
5712 so that if an exception is raised in the command <literal>body</literal>,
5713 the variable <literal>ex</literal> is bound to the value of the exception
5714 and the command <literal>handler</literal>,
5715 which typically refers to <literal>ex</literal>, is entered.
5716 Though the syntax here looks like a functional lambda,
5717 we are talking about commands, and something different is going on.
5718 The input to the arrow represented by a command consists of values for
5719 the free local variables in the command, plus a stack of anonymous values.
5720 In all the prior examples, this stack was empty.
5721 In the second argument to <function>handleA</function>,
5722 this stack consists of one value, the value of the exception.
5723 The command form of lambda merely gives this value a name.
5728 the values on the stack are paired to the right of the environment.
5729 So operators like <function>handleA</function> that pass
5730 extra inputs to their subcommands can be designed for use with the notation
5731 by pairing the values with the environment in this way.
5732 More precisely, the type of each argument of the operator (and its result)
5733 should have the form
5735 a (...(e,t1), ... tn) t
5737 where <replaceable>e</replaceable> is a polymorphic variable
5738 (representing the environment)
5739 and <replaceable>ti</replaceable> are the types of the values on the stack,
5740 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5741 The polymorphic variable <replaceable>e</replaceable> must not occur in
5742 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5743 <replaceable>t</replaceable>.
5744 However the arrows involved need not be the same.
5745 Here are some more examples of suitable operators:
5747 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5748 runReader :: ... => a e c -> a' (e,State) c
5749 runState :: ... => a e c -> a' (e,State) (c,State)
5751 We can supply the extra input required by commands built with the last two
5752 by applying them to ordinary expressions, as in
5756 (|runReader (do { ... })|) s
5758 which adds <literal>s</literal> to the stack of inputs to the command
5759 built using <function>runReader</function>.
5763 The command versions of lambda abstraction and application are analogous to
5764 the expression versions.
5765 In particular, the beta and eta rules describe equivalences of commands.
5766 These three features (operators, lambda abstraction and application)
5767 are the core of the notation; everything else can be built using them,
5768 though the results would be somewhat clumsy.
5769 For example, we could simulate <literal>do</literal>-notation by defining
5771 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5772 u `bind` f = returnA &&& u >>> f
5774 bind_ :: Arrow a => a e b -> a e c -> a e c
5775 u `bind_` f = u `bind` (arr fst >>> f)
5777 We could simulate <literal>if</literal> by defining
5779 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5780 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5787 <title>Differences with the paper</title>
5792 <para>Instead of a single form of arrow application (arrow tail) with two
5793 translations, the implementation provides two forms
5794 <quote><literal>-<</literal></quote> (first-order)
5795 and <quote><literal>-<<</literal></quote> (higher-order).
5800 <para>User-defined operators are flagged with banana brackets instead of
5801 a new <literal>form</literal> keyword.
5810 <title>Portability</title>
5813 Although only GHC implements arrow notation directly,
5814 there is also a preprocessor
5816 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5817 that translates arrow notation into Haskell 98
5818 for use with other Haskell systems.
5819 You would still want to check arrow programs with GHC;
5820 tracing type errors in the preprocessor output is not easy.
5821 Modules intended for both GHC and the preprocessor must observe some
5822 additional restrictions:
5827 The module must import
5828 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5834 The preprocessor cannot cope with other Haskell extensions.
5835 These would have to go in separate modules.
5841 Because the preprocessor targets Haskell (rather than Core),
5842 <literal>let</literal>-bound variables are monomorphic.
5853 <!-- ==================== BANG PATTERNS ================= -->
5855 <sect1 id="bang-patterns">
5856 <title>Bang patterns
5857 <indexterm><primary>Bang patterns</primary></indexterm>
5859 <para>GHC supports an extension of pattern matching called <emphasis>bang
5860 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5862 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5863 prime feature description</ulink> contains more discussion and examples
5864 than the material below.
5867 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5870 <sect2 id="bang-patterns-informal">
5871 <title>Informal description of bang patterns
5874 The main idea is to add a single new production to the syntax of patterns:
5878 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5879 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5884 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5885 whereas without the bang it would be lazy.
5886 Bang patterns can be nested of course:
5890 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5891 <literal>y</literal>.
5892 A bang only really has an effect if it precedes a variable or wild-card pattern:
5897 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5898 forces evaluation anyway does nothing.
5900 Bang patterns work in <literal>case</literal> expressions too, of course:
5902 g5 x = let y = f x in body
5903 g6 x = case f x of { y -> body }
5904 g7 x = case f x of { !y -> body }
5906 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5907 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5908 result, and then evaluates <literal>body</literal>.
5910 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5911 definitions too. For example:
5915 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5916 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5917 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5918 in a function argument <literal>![x,y]</literal> means the
5919 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5920 is part of the syntax of <literal>let</literal> bindings.
5925 <sect2 id="bang-patterns-sem">
5926 <title>Syntax and semantics
5930 We add a single new production to the syntax of patterns:
5934 There is one problem with syntactic ambiguity. Consider:
5938 Is this a definition of the infix function "<literal>(!)</literal>",
5939 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5940 ambiguity in favour of the latter. If you want to define
5941 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5946 The semantics of Haskell pattern matching is described in <ulink
5947 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5948 Section 3.17.2</ulink> of the Haskell Report. To this description add
5949 one extra item 10, saying:
5950 <itemizedlist><listitem><para>Matching
5951 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5952 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5953 <listitem><para>otherwise, <literal>pat</literal> is matched against
5954 <literal>v</literal></para></listitem>
5956 </para></listitem></itemizedlist>
5957 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5958 Section 3.17.3</ulink>, add a new case (t):
5960 case v of { !pat -> e; _ -> e' }
5961 = v `seq` case v of { pat -> e; _ -> e' }
5964 That leaves let expressions, whose translation is given in
5965 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
5967 of the Haskell Report.
5968 In the translation box, first apply
5969 the following transformation: for each pattern <literal>pi</literal> that is of
5970 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5971 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5972 have a bang at the top, apply the rules in the existing box.
5974 <para>The effect of the let rule is to force complete matching of the pattern
5975 <literal>qi</literal> before evaluation of the body is begun. The bang is
5976 retained in the translated form in case <literal>qi</literal> is a variable,
5984 The let-binding can be recursive. However, it is much more common for
5985 the let-binding to be non-recursive, in which case the following law holds:
5986 <literal>(let !p = rhs in body)</literal>
5988 <literal>(case rhs of !p -> body)</literal>
5991 A pattern with a bang at the outermost level is not allowed at the top level of
5997 <!-- ==================== ASSERTIONS ================= -->
5999 <sect1 id="assertions">
6001 <indexterm><primary>Assertions</primary></indexterm>
6005 If you want to make use of assertions in your standard Haskell code, you
6006 could define a function like the following:
6012 assert :: Bool -> a -> a
6013 assert False x = error "assertion failed!"
6020 which works, but gives you back a less than useful error message --
6021 an assertion failed, but which and where?
6025 One way out is to define an extended <function>assert</function> function which also
6026 takes a descriptive string to include in the error message and
6027 perhaps combine this with the use of a pre-processor which inserts
6028 the source location where <function>assert</function> was used.
6032 Ghc offers a helping hand here, doing all of this for you. For every
6033 use of <function>assert</function> in the user's source:
6039 kelvinToC :: Double -> Double
6040 kelvinToC k = assert (k >= 0.0) (k+273.15)
6046 Ghc will rewrite this to also include the source location where the
6053 assert pred val ==> assertError "Main.hs|15" pred val
6059 The rewrite is only performed by the compiler when it spots
6060 applications of <function>Control.Exception.assert</function>, so you
6061 can still define and use your own versions of
6062 <function>assert</function>, should you so wish. If not, import
6063 <literal>Control.Exception</literal> to make use
6064 <function>assert</function> in your code.
6068 GHC ignores assertions when optimisation is turned on with the
6069 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6070 <literal>assert pred e</literal> will be rewritten to
6071 <literal>e</literal>. You can also disable assertions using the
6072 <option>-fignore-asserts</option>
6073 option<indexterm><primary><option>-fignore-asserts</option></primary>
6074 </indexterm>.</para>
6077 Assertion failures can be caught, see the documentation for the
6078 <literal>Control.Exception</literal> library for the details.
6084 <!-- =============================== PRAGMAS =========================== -->
6086 <sect1 id="pragmas">
6087 <title>Pragmas</title>
6089 <indexterm><primary>pragma</primary></indexterm>
6091 <para>GHC supports several pragmas, or instructions to the
6092 compiler placed in the source code. Pragmas don't normally affect
6093 the meaning of the program, but they might affect the efficiency
6094 of the generated code.</para>
6096 <para>Pragmas all take the form
6098 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6100 where <replaceable>word</replaceable> indicates the type of
6101 pragma, and is followed optionally by information specific to that
6102 type of pragma. Case is ignored in
6103 <replaceable>word</replaceable>. The various values for
6104 <replaceable>word</replaceable> that GHC understands are described
6105 in the following sections; any pragma encountered with an
6106 unrecognised <replaceable>word</replaceable> is (silently)
6107 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6108 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6110 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6111 pragma must precede the <literal>module</literal> keyword in the file.
6112 There can be as many file-header pragmas as you please, and they can be
6113 preceded or followed by comments.</para>
6115 <sect2 id="language-pragma">
6116 <title>LANGUAGE pragma</title>
6118 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6119 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6121 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6123 It is the intention that all Haskell compilers support the
6124 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6125 all extensions are supported by all compilers, of
6126 course. The <literal>LANGUAGE</literal> pragma should be used instead
6127 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6129 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6131 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6133 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6135 <para>Every language extension can also be turned into a command-line flag
6136 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6137 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6140 <para>A list of all supported language extensions can be obtained by invoking
6141 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6143 <para>Any extension from the <literal>Extension</literal> type defined in
6145 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6146 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6150 <sect2 id="options-pragma">
6151 <title>OPTIONS_GHC pragma</title>
6152 <indexterm><primary>OPTIONS_GHC</primary>
6154 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6157 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6158 additional options that are given to the compiler when compiling
6159 this source file. See <xref linkend="source-file-options"/> for
6162 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6163 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6166 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6168 <sect2 id="include-pragma">
6169 <title>INCLUDE pragma</title>
6171 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6172 of C header files that should be <literal>#include</literal>'d into
6173 the C source code generated by the compiler for the current module (if
6174 compiling via C). For example:</para>
6177 {-# INCLUDE "foo.h" #-}
6178 {-# INCLUDE <stdio.h> #-}</programlisting>
6180 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6182 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6183 to the <option>-#include</option> option (<xref
6184 linkend="options-C-compiler" />), because the
6185 <literal>INCLUDE</literal> pragma is understood by other
6186 compilers. Yet another alternative is to add the include file to each
6187 <literal>foreign import</literal> declaration in your code, but we
6188 don't recommend using this approach with GHC.</para>
6191 <sect2 id="warning-deprecated-pragma">
6192 <title>WARNING and DEPRECATED pragmas</title>
6193 <indexterm><primary>WARNING</primary></indexterm>
6194 <indexterm><primary>DEPRECATED</primary></indexterm>
6196 <para>The WARNING pragma allows you to attach an arbitrary warning
6197 to a particular function, class, or type.
6198 A DEPRECATED pragma lets you specify that
6199 a particular function, class, or type is deprecated.
6200 There are two ways of using these pragmas.
6204 <para>You can work on an entire module thus:</para>
6206 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6211 module Wibble {-# WARNING "This is an unstable interface." #-} where
6214 <para>When you compile any module that import
6215 <literal>Wibble</literal>, GHC will print the specified
6220 <para>You can attach a warning to a function, class, type, or data constructor, with the
6221 following top-level declarations:</para>
6223 {-# DEPRECATED f, C, T "Don't use these" #-}
6224 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6226 <para>When you compile any module that imports and uses any
6227 of the specified entities, GHC will print the specified
6229 <para> You can only attach to entities declared at top level in the module
6230 being compiled, and you can only use unqualified names in the list of
6231 entities. A capitalised name, such as <literal>T</literal>
6232 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6233 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6234 both are in scope. If both are in scope, there is currently no way to
6235 specify one without the other (c.f. fixities
6236 <xref linkend="infix-tycons"/>).</para>
6239 Warnings and deprecations are not reported for
6240 (a) uses within the defining module, and
6241 (b) uses in an export list.
6242 The latter reduces spurious complaints within a library
6243 in which one module gathers together and re-exports
6244 the exports of several others.
6246 <para>You can suppress the warnings with the flag
6247 <option>-fno-warn-warnings-deprecations</option>.</para>
6250 <sect2 id="inline-noinline-pragma">
6251 <title>INLINE and NOINLINE pragmas</title>
6253 <para>These pragmas control the inlining of function
6256 <sect3 id="inline-pragma">
6257 <title>INLINE pragma</title>
6258 <indexterm><primary>INLINE</primary></indexterm>
6260 <para>GHC (with <option>-O</option>, as always) tries to
6261 inline (or “unfold”) functions/values that are
6262 “small enough,” thus avoiding the call overhead
6263 and possibly exposing other more-wonderful optimisations.
6264 Normally, if GHC decides a function is “too
6265 expensive” to inline, it will not do so, nor will it
6266 export that unfolding for other modules to use.</para>
6268 <para>The sledgehammer you can bring to bear is the
6269 <literal>INLINE</literal><indexterm><primary>INLINE
6270 pragma</primary></indexterm> pragma, used thusly:</para>
6273 key_function :: Int -> String -> (Bool, Double)
6274 {-# INLINE key_function #-}
6277 <para>The major effect of an <literal>INLINE</literal> pragma
6278 is to declare a function's “cost” to be very low.
6279 The normal unfolding machinery will then be very keen to
6280 inline it. However, an <literal>INLINE</literal> pragma for a
6281 function "<literal>f</literal>" has a number of other effects:
6284 No functions are inlined into <literal>f</literal>. Otherwise
6285 GHC might inline a big function into <literal>f</literal>'s right hand side,
6286 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6289 The float-in, float-out, and common-sub-expression transformations are not
6290 applied to the body of <literal>f</literal>.
6293 An INLINE function is not worker/wrappered by strictness analysis.
6294 It's going to be inlined wholesale instead.
6297 All of these effects are aimed at ensuring that what gets inlined is
6298 exactly what you asked for, no more and no less.
6300 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6301 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6302 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6303 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6304 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6305 when there is no choice even an INLINE function can be selected, in which case
6306 the INLINE pragma is ignored.
6307 For example, for a self-recursive function, the loop breaker can only be the function
6308 itself, so an INLINE pragma is always ignored.</para>
6310 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6311 function can be put anywhere its type signature could be
6314 <para><literal>INLINE</literal> pragmas are a particularly
6316 <literal>then</literal>/<literal>return</literal> (or
6317 <literal>bind</literal>/<literal>unit</literal>) functions in
6318 a monad. For example, in GHC's own
6319 <literal>UniqueSupply</literal> monad code, we have:</para>
6322 {-# INLINE thenUs #-}
6323 {-# INLINE returnUs #-}
6326 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6327 linkend="noinline-pragma"/>).</para>
6329 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
6330 so if you want your code to be HBC-compatible you'll have to surround
6331 the pragma with C pre-processor directives
6332 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
6336 <sect3 id="noinline-pragma">
6337 <title>NOINLINE pragma</title>
6339 <indexterm><primary>NOINLINE</primary></indexterm>
6340 <indexterm><primary>NOTINLINE</primary></indexterm>
6342 <para>The <literal>NOINLINE</literal> pragma does exactly what
6343 you'd expect: it stops the named function from being inlined
6344 by the compiler. You shouldn't ever need to do this, unless
6345 you're very cautious about code size.</para>
6347 <para><literal>NOTINLINE</literal> is a synonym for
6348 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6349 specified by Haskell 98 as the standard way to disable
6350 inlining, so it should be used if you want your code to be
6354 <sect3 id="phase-control">
6355 <title>Phase control</title>
6357 <para> Sometimes you want to control exactly when in GHC's
6358 pipeline the INLINE pragma is switched on. Inlining happens
6359 only during runs of the <emphasis>simplifier</emphasis>. Each
6360 run of the simplifier has a different <emphasis>phase
6361 number</emphasis>; the phase number decreases towards zero.
6362 If you use <option>-dverbose-core2core</option> you'll see the
6363 sequence of phase numbers for successive runs of the
6364 simplifier. In an INLINE pragma you can optionally specify a
6368 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6369 <literal>f</literal>
6370 until phase <literal>k</literal>, but from phase
6371 <literal>k</literal> onwards be very keen to inline it.
6374 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6375 <literal>f</literal>
6376 until phase <literal>k</literal>, but from phase
6377 <literal>k</literal> onwards do not inline it.
6380 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6381 <literal>f</literal>
6382 until phase <literal>k</literal>, but from phase
6383 <literal>k</literal> onwards be willing to inline it (as if
6384 there was no pragma).
6387 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6388 <literal>f</literal>
6389 until phase <literal>k</literal>, but from phase
6390 <literal>k</literal> onwards do not inline it.
6393 The same information is summarised here:
6395 -- Before phase 2 Phase 2 and later
6396 {-# INLINE [2] f #-} -- No Yes
6397 {-# INLINE [~2] f #-} -- Yes No
6398 {-# NOINLINE [2] f #-} -- No Maybe
6399 {-# NOINLINE [~2] f #-} -- Maybe No
6401 {-# INLINE f #-} -- Yes Yes
6402 {-# NOINLINE f #-} -- No No
6404 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6405 function body is small, or it is applied to interesting-looking arguments etc).
6406 Another way to understand the semantics is this:
6408 <listitem><para>For both INLINE and NOINLINE, the phase number says
6409 when inlining is allowed at all.</para></listitem>
6410 <listitem><para>The INLINE pragma has the additional effect of making the
6411 function body look small, so that when inlining is allowed it is very likely to
6416 <para>The same phase-numbering control is available for RULES
6417 (<xref linkend="rewrite-rules"/>).</para>
6421 <sect2 id="line-pragma">
6422 <title>LINE pragma</title>
6424 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6425 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6426 <para>This pragma is similar to C's <literal>#line</literal>
6427 pragma, and is mainly for use in automatically generated Haskell
6428 code. It lets you specify the line number and filename of the
6429 original code; for example</para>
6431 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6433 <para>if you'd generated the current file from something called
6434 <filename>Foo.vhs</filename> and this line corresponds to line
6435 42 in the original. GHC will adjust its error messages to refer
6436 to the line/file named in the <literal>LINE</literal>
6441 <title>RULES pragma</title>
6443 <para>The RULES pragma lets you specify rewrite rules. It is
6444 described in <xref linkend="rewrite-rules"/>.</para>
6447 <sect2 id="specialize-pragma">
6448 <title>SPECIALIZE pragma</title>
6450 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6451 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6452 <indexterm><primary>overloading, death to</primary></indexterm>
6454 <para>(UK spelling also accepted.) For key overloaded
6455 functions, you can create extra versions (NB: more code space)
6456 specialised to particular types. Thus, if you have an
6457 overloaded function:</para>
6460 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6463 <para>If it is heavily used on lists with
6464 <literal>Widget</literal> keys, you could specialise it as
6468 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6471 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6472 be put anywhere its type signature could be put.</para>
6474 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6475 (a) a specialised version of the function and (b) a rewrite rule
6476 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6477 un-specialised function into a call to the specialised one.</para>
6479 <para>The type in a SPECIALIZE pragma can be any type that is less
6480 polymorphic than the type of the original function. In concrete terms,
6481 if the original function is <literal>f</literal> then the pragma
6483 {-# SPECIALIZE f :: <type> #-}
6485 is valid if and only if the definition
6487 f_spec :: <type>
6490 is valid. Here are some examples (where we only give the type signature
6491 for the original function, not its code):
6493 f :: Eq a => a -> b -> b
6494 {-# SPECIALISE f :: Int -> b -> b #-}
6496 g :: (Eq a, Ix b) => a -> b -> b
6497 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6499 h :: Eq a => a -> a -> a
6500 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6502 The last of these examples will generate a
6503 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6504 well. If you use this kind of specialisation, let us know how well it works.
6507 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6508 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6509 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6510 The <literal>INLINE</literal> pragma affects the specialised version of the
6511 function (only), and applies even if the function is recursive. The motivating
6514 -- A GADT for arrays with type-indexed representation
6516 ArrInt :: !Int -> ByteArray# -> Arr Int
6517 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6519 (!:) :: Arr e -> Int -> e
6520 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6521 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6522 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6523 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6525 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6526 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6527 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6528 the specialised function will be inlined. It has two calls to
6529 <literal>(!:)</literal>,
6530 both at type <literal>Int</literal>. Both these calls fire the first
6531 specialisation, whose body is also inlined. The result is a type-based
6532 unrolling of the indexing function.</para>
6533 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6534 on an ordinarily-recursive function.</para>
6536 <para>Note: In earlier versions of GHC, it was possible to provide your own
6537 specialised function for a given type:
6540 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6543 This feature has been removed, as it is now subsumed by the
6544 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6548 <sect2 id="specialize-instance-pragma">
6549 <title>SPECIALIZE instance pragma
6553 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6554 <indexterm><primary>overloading, death to</primary></indexterm>
6555 Same idea, except for instance declarations. For example:
6558 instance (Eq a) => Eq (Foo a) where {
6559 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6563 The pragma must occur inside the <literal>where</literal> part
6564 of the instance declaration.
6567 Compatible with HBC, by the way, except perhaps in the placement
6573 <sect2 id="unpack-pragma">
6574 <title>UNPACK pragma</title>
6576 <indexterm><primary>UNPACK</primary></indexterm>
6578 <para>The <literal>UNPACK</literal> indicates to the compiler
6579 that it should unpack the contents of a constructor field into
6580 the constructor itself, removing a level of indirection. For
6584 data T = T {-# UNPACK #-} !Float
6585 {-# UNPACK #-} !Float
6588 <para>will create a constructor <literal>T</literal> containing
6589 two unboxed floats. This may not always be an optimisation: if
6590 the <function>T</function> constructor is scrutinised and the
6591 floats passed to a non-strict function for example, they will
6592 have to be reboxed (this is done automatically by the
6595 <para>Unpacking constructor fields should only be used in
6596 conjunction with <option>-O</option>, in order to expose
6597 unfoldings to the compiler so the reboxing can be removed as
6598 often as possible. For example:</para>
6602 f (T f1 f2) = f1 + f2
6605 <para>The compiler will avoid reboxing <function>f1</function>
6606 and <function>f2</function> by inlining <function>+</function>
6607 on floats, but only when <option>-O</option> is on.</para>
6609 <para>Any single-constructor data is eligible for unpacking; for
6613 data T = T {-# UNPACK #-} !(Int,Int)
6616 <para>will store the two <literal>Int</literal>s directly in the
6617 <function>T</function> constructor, by flattening the pair.
6618 Multi-level unpacking is also supported:
6621 data T = T {-# UNPACK #-} !S
6622 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6625 will store two unboxed <literal>Int#</literal>s
6626 directly in the <function>T</function> constructor. The
6627 unpacker can see through newtypes, too.</para>
6629 <para>If a field cannot be unpacked, you will not get a warning,
6630 so it might be an idea to check the generated code with
6631 <option>-ddump-simpl</option>.</para>
6633 <para>See also the <option>-funbox-strict-fields</option> flag,
6634 which essentially has the effect of adding
6635 <literal>{-# UNPACK #-}</literal> to every strict
6636 constructor field.</para>
6639 <sect2 id="source-pragma">
6640 <title>SOURCE pragma</title>
6642 <indexterm><primary>SOURCE</primary></indexterm>
6643 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6644 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6650 <!-- ======================= REWRITE RULES ======================== -->
6652 <sect1 id="rewrite-rules">
6653 <title>Rewrite rules
6655 <indexterm><primary>RULES pragma</primary></indexterm>
6656 <indexterm><primary>pragma, RULES</primary></indexterm>
6657 <indexterm><primary>rewrite rules</primary></indexterm></title>
6660 The programmer can specify rewrite rules as part of the source program
6666 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6671 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
6672 If you need more information, then <option>-ddump-rule-firings</option> shows you
6673 each individual rule firing in detail.
6677 <title>Syntax</title>
6680 From a syntactic point of view:
6686 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6687 may be generated by the layout rule).
6693 The layout rule applies in a pragma.
6694 Currently no new indentation level
6695 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6696 you must lay out the starting in the same column as the enclosing definitions.
6699 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6700 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6703 Furthermore, the closing <literal>#-}</literal>
6704 should start in a column to the right of the opening <literal>{-#</literal>.
6710 Each rule has a name, enclosed in double quotes. The name itself has
6711 no significance at all. It is only used when reporting how many times the rule fired.
6717 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6718 immediately after the name of the rule. Thus:
6721 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6724 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6725 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6734 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6735 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6736 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6737 by spaces, just like in a type <literal>forall</literal>.
6743 A pattern variable may optionally have a type signature.
6744 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6745 For example, here is the <literal>foldr/build</literal> rule:
6748 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6749 foldr k z (build g) = g k z
6752 Since <function>g</function> has a polymorphic type, it must have a type signature.
6759 The left hand side of a rule must consist of a top-level variable applied
6760 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6763 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6764 "wrong2" forall f. f True = True
6767 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6774 A rule does not need to be in the same module as (any of) the
6775 variables it mentions, though of course they need to be in scope.
6781 All rules are implicitly exported from the module, and are therefore
6782 in force in any module that imports the module that defined the rule, directly
6783 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6784 in force when compiling A.) The situation is very similar to that for instance
6792 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
6793 any other flag settings. Furthermore, inside a RULE, the language extension
6794 <option>-XScopedTypeVariables</option> is automatically enabled; see
6795 <xref linkend="scoped-type-variables"/>.
6801 Like other pragmas, RULE pragmas are always checked for scope errors, and
6802 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
6803 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
6804 if the <option>-fenable-rewrite-rules</option> flag is
6805 on (see <xref linkend="rule-semantics"/>).
6814 <sect2 id="rule-semantics">
6815 <title>Semantics</title>
6818 From a semantic point of view:
6823 Rules are enabled (that is, used during optimisation)
6824 by the <option>-fenable-rewrite-rules</option> flag.
6825 This flag is implied by <option>-O</option>, and may be switched
6826 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
6827 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
6828 may not do what you expect, though, because without <option>-O</option> GHC
6829 ignores all optimisation information in interface files;
6830 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
6831 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
6832 has no effect on parsing or typechecking.
6838 Rules are regarded as left-to-right rewrite rules.
6839 When GHC finds an expression that is a substitution instance of the LHS
6840 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6841 By "a substitution instance" we mean that the LHS can be made equal to the
6842 expression by substituting for the pattern variables.
6849 GHC makes absolutely no attempt to verify that the LHS and RHS
6850 of a rule have the same meaning. That is undecidable in general, and
6851 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6858 GHC makes no attempt to make sure that the rules are confluent or
6859 terminating. For example:
6862 "loop" forall x y. f x y = f y x
6865 This rule will cause the compiler to go into an infinite loop.
6872 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6878 GHC currently uses a very simple, syntactic, matching algorithm
6879 for matching a rule LHS with an expression. It seeks a substitution
6880 which makes the LHS and expression syntactically equal modulo alpha
6881 conversion. The pattern (rule), but not the expression, is eta-expanded if
6882 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6883 But not beta conversion (that's called higher-order matching).
6887 Matching is carried out on GHC's intermediate language, which includes
6888 type abstractions and applications. So a rule only matches if the
6889 types match too. See <xref linkend="rule-spec"/> below.
6895 GHC keeps trying to apply the rules as it optimises the program.
6896 For example, consider:
6905 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6906 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6907 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6908 not be substituted, and the rule would not fire.
6915 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
6916 results. Consider this (artificial) example
6919 {-# RULES "f" f True = False #-}
6925 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
6930 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
6932 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
6933 would have been a better chance that <literal>f</literal>'s RULE might fire.
6936 The way to get predictable behaviour is to use a NOINLINE
6937 pragma on <literal>f</literal>, to ensure
6938 that it is not inlined until its RULEs have had a chance to fire.
6948 <title>List fusion</title>
6951 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6952 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6953 intermediate list should be eliminated entirely.
6957 The following are good producers:
6969 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6975 Explicit lists (e.g. <literal>[True, False]</literal>)
6981 The cons constructor (e.g <literal>3:4:[]</literal>)
6987 <function>++</function>
6993 <function>map</function>
6999 <function>take</function>, <function>filter</function>
7005 <function>iterate</function>, <function>repeat</function>
7011 <function>zip</function>, <function>zipWith</function>
7020 The following are good consumers:
7032 <function>array</function> (on its second argument)
7038 <function>++</function> (on its first argument)
7044 <function>foldr</function>
7050 <function>map</function>
7056 <function>take</function>, <function>filter</function>
7062 <function>concat</function>
7068 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7074 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7075 will fuse with one but not the other)
7081 <function>partition</function>
7087 <function>head</function>
7093 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7099 <function>sequence_</function>
7105 <function>msum</function>
7111 <function>sortBy</function>
7120 So, for example, the following should generate no intermediate lists:
7123 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7129 This list could readily be extended; if there are Prelude functions that you use
7130 a lot which are not included, please tell us.
7134 If you want to write your own good consumers or producers, look at the
7135 Prelude definitions of the above functions to see how to do so.
7140 <sect2 id="rule-spec">
7141 <title>Specialisation
7145 Rewrite rules can be used to get the same effect as a feature
7146 present in earlier versions of GHC.
7147 For example, suppose that:
7150 genericLookup :: Ord a => Table a b -> a -> b
7151 intLookup :: Table Int b -> Int -> b
7154 where <function>intLookup</function> is an implementation of
7155 <function>genericLookup</function> that works very fast for
7156 keys of type <literal>Int</literal>. You might wish
7157 to tell GHC to use <function>intLookup</function> instead of
7158 <function>genericLookup</function> whenever the latter was called with
7159 type <literal>Table Int b -> Int -> b</literal>.
7160 It used to be possible to write
7163 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7166 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7169 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7172 This slightly odd-looking rule instructs GHC to replace
7173 <function>genericLookup</function> by <function>intLookup</function>
7174 <emphasis>whenever the types match</emphasis>.
7175 What is more, this rule does not need to be in the same
7176 file as <function>genericLookup</function>, unlike the
7177 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7178 have an original definition available to specialise).
7181 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7182 <function>intLookup</function> really behaves as a specialised version
7183 of <function>genericLookup</function>!!!</para>
7185 <para>An example in which using <literal>RULES</literal> for
7186 specialisation will Win Big:
7189 toDouble :: Real a => a -> Double
7190 toDouble = fromRational . toRational
7192 {-# RULES "toDouble/Int" toDouble = i2d #-}
7193 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7196 The <function>i2d</function> function is virtually one machine
7197 instruction; the default conversion—via an intermediate
7198 <literal>Rational</literal>—is obscenely expensive by
7205 <title>Controlling what's going on</title>
7213 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7219 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7220 If you add <option>-dppr-debug</option> you get a more detailed listing.
7226 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7229 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7230 {-# INLINE build #-}
7234 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7235 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7236 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7237 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7244 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7245 see how to write rules that will do fusion and yet give an efficient
7246 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7256 <sect2 id="core-pragma">
7257 <title>CORE pragma</title>
7259 <indexterm><primary>CORE pragma</primary></indexterm>
7260 <indexterm><primary>pragma, CORE</primary></indexterm>
7261 <indexterm><primary>core, annotation</primary></indexterm>
7264 The external core format supports <quote>Note</quote> annotations;
7265 the <literal>CORE</literal> pragma gives a way to specify what these
7266 should be in your Haskell source code. Syntactically, core
7267 annotations are attached to expressions and take a Haskell string
7268 literal as an argument. The following function definition shows an
7272 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7275 Semantically, this is equivalent to:
7283 However, when external core is generated (via
7284 <option>-fext-core</option>), there will be Notes attached to the
7285 expressions <function>show</function> and <varname>x</varname>.
7286 The core function declaration for <function>f</function> is:
7290 f :: %forall a . GHCziShow.ZCTShow a ->
7291 a -> GHCziBase.ZMZN GHCziBase.Char =
7292 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7294 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7296 (tpl1::GHCziBase.Int ->
7298 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7300 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7301 (tpl3::GHCziBase.ZMZN a ->
7302 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7310 Here, we can see that the function <function>show</function> (which
7311 has been expanded out to a case expression over the Show dictionary)
7312 has a <literal>%note</literal> attached to it, as does the
7313 expression <varname>eta</varname> (which used to be called
7314 <varname>x</varname>).
7321 <sect1 id="special-ids">
7322 <title>Special built-in functions</title>
7323 <para>GHC has a few built-in functions with special behaviour. These
7324 are now described in the module <ulink
7325 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7326 in the library documentation.</para>
7330 <sect1 id="generic-classes">
7331 <title>Generic classes</title>
7334 The ideas behind this extension are described in detail in "Derivable type classes",
7335 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7336 An example will give the idea:
7344 fromBin :: [Int] -> (a, [Int])
7346 toBin {| Unit |} Unit = []
7347 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7348 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7349 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7351 fromBin {| Unit |} bs = (Unit, bs)
7352 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7353 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7354 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7355 (y,bs'') = fromBin bs'
7358 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7359 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7360 which are defined thus in the library module <literal>Generics</literal>:
7364 data a :+: b = Inl a | Inr b
7365 data a :*: b = a :*: b
7368 Now you can make a data type into an instance of Bin like this:
7370 instance (Bin a, Bin b) => Bin (a,b)
7371 instance Bin a => Bin [a]
7373 That is, just leave off the "where" clause. Of course, you can put in the
7374 where clause and over-ride whichever methods you please.
7378 <title> Using generics </title>
7379 <para>To use generics you need to</para>
7382 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7383 <option>-XGenerics</option> (to generate extra per-data-type code),
7384 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7388 <para>Import the module <literal>Generics</literal> from the
7389 <literal>lang</literal> package. This import brings into
7390 scope the data types <literal>Unit</literal>,
7391 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7392 don't need this import if you don't mention these types
7393 explicitly; for example, if you are simply giving instance
7394 declarations.)</para>
7399 <sect2> <title> Changes wrt the paper </title>
7401 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7402 can be written infix (indeed, you can now use
7403 any operator starting in a colon as an infix type constructor). Also note that
7404 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7405 Finally, note that the syntax of the type patterns in the class declaration
7406 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7407 alone would ambiguous when they appear on right hand sides (an extension we
7408 anticipate wanting).
7412 <sect2> <title>Terminology and restrictions</title>
7414 Terminology. A "generic default method" in a class declaration
7415 is one that is defined using type patterns as above.
7416 A "polymorphic default method" is a default method defined as in Haskell 98.
7417 A "generic class declaration" is a class declaration with at least one
7418 generic default method.
7426 Alas, we do not yet implement the stuff about constructor names and
7433 A generic class can have only one parameter; you can't have a generic
7434 multi-parameter class.
7440 A default method must be defined entirely using type patterns, or entirely
7441 without. So this is illegal:
7444 op :: a -> (a, Bool)
7445 op {| Unit |} Unit = (Unit, True)
7448 However it is perfectly OK for some methods of a generic class to have
7449 generic default methods and others to have polymorphic default methods.
7455 The type variable(s) in the type pattern for a generic method declaration
7456 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:
7460 op {| p :*: q |} (x :*: y) = op (x :: p)
7468 The type patterns in a generic default method must take one of the forms:
7474 where "a" and "b" are type variables. Furthermore, all the type patterns for
7475 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7476 must use the same type variables. So this is illegal:
7480 op {| a :+: b |} (Inl x) = True
7481 op {| p :+: q |} (Inr y) = False
7483 The type patterns must be identical, even in equations for different methods of the class.
7484 So this too is illegal:
7488 op1 {| a :*: b |} (x :*: y) = True
7491 op2 {| p :*: q |} (x :*: y) = False
7493 (The reason for this restriction is that we gather all the equations for a particular type constructor
7494 into a single generic instance declaration.)
7500 A generic method declaration must give a case for each of the three type constructors.
7506 The type for a generic method can be built only from:
7508 <listitem> <para> Function arrows </para> </listitem>
7509 <listitem> <para> Type variables </para> </listitem>
7510 <listitem> <para> Tuples </para> </listitem>
7511 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7513 Here are some example type signatures for generic methods:
7516 op2 :: Bool -> (a,Bool)
7517 op3 :: [Int] -> a -> a
7520 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7524 This restriction is an implementation restriction: we just haven't got around to
7525 implementing the necessary bidirectional maps over arbitrary type constructors.
7526 It would be relatively easy to add specific type constructors, such as Maybe and list,
7527 to the ones that are allowed.</para>
7532 In an instance declaration for a generic class, the idea is that the compiler
7533 will fill in the methods for you, based on the generic templates. However it can only
7538 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7543 No constructor of the instance type has unboxed fields.
7547 (Of course, these things can only arise if you are already using GHC extensions.)
7548 However, you can still give an instance declarations for types which break these rules,
7549 provided you give explicit code to override any generic default methods.
7557 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7558 what the compiler does with generic declarations.
7563 <sect2> <title> Another example </title>
7565 Just to finish with, here's another example I rather like:
7569 nCons {| Unit |} _ = 1
7570 nCons {| a :*: b |} _ = 1
7571 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7574 tag {| Unit |} _ = 1
7575 tag {| a :*: b |} _ = 1
7576 tag {| a :+: b |} (Inl x) = tag x
7577 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7583 <sect1 id="monomorphism">
7584 <title>Control over monomorphism</title>
7586 <para>GHC supports two flags that control the way in which generalisation is
7587 carried out at let and where bindings.
7591 <title>Switching off the dreaded Monomorphism Restriction</title>
7592 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7594 <para>Haskell's monomorphism restriction (see
7595 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7597 of the Haskell Report)
7598 can be completely switched off by
7599 <option>-XNoMonomorphismRestriction</option>.
7604 <title>Monomorphic pattern bindings</title>
7605 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7606 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7608 <para> As an experimental change, we are exploring the possibility of
7609 making pattern bindings monomorphic; that is, not generalised at all.
7610 A pattern binding is a binding whose LHS has no function arguments,
7611 and is not a simple variable. For example:
7613 f x = x -- Not a pattern binding
7614 f = \x -> x -- Not a pattern binding
7615 f :: Int -> Int = \x -> x -- Not a pattern binding
7617 (g,h) = e -- A pattern binding
7618 (f) = e -- A pattern binding
7619 [x] = e -- A pattern binding
7621 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7622 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7631 ;;; Local Variables: ***
7633 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7634 ;;; ispell-local-dictionary: "british" ***
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