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 result of the <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.
2454 <!-- ====================== End of Generalised algebraic data types ======================= -->
2456 <sect1 id="deriving">
2457 <title>Extensions to the "deriving" mechanism</title>
2459 <sect2 id="deriving-inferred">
2460 <title>Inferred context for deriving clauses</title>
2463 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2466 data T0 f a = MkT0 a deriving( Eq )
2467 data T1 f a = MkT1 (f a) deriving( Eq )
2468 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2470 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2472 instance Eq a => Eq (T0 f a) where ...
2473 instance Eq (f a) => Eq (T1 f a) where ...
2474 instance Eq (f (f a)) => Eq (T2 f a) where ...
2476 The first of these is obviously fine. The second is still fine, although less obviously.
2477 The third is not Haskell 98, and risks losing termination of instances.
2480 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2481 each constraint in the inferred instance context must consist only of type variables,
2482 with no repetitions.
2485 This rule is applied regardless of flags. If you want a more exotic context, you can write
2486 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2490 <sect2 id="stand-alone-deriving">
2491 <title>Stand-alone deriving declarations</title>
2494 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2496 data Foo a = Bar a | Baz String
2498 deriving instance Eq a => Eq (Foo a)
2500 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2501 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2502 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2503 exactly as you would in an ordinary instance declaration.
2504 (In contrast the context is inferred in a <literal>deriving</literal> clause
2505 attached to a data type declaration.)
2507 A <literal>deriving instance</literal> declaration
2508 must obey the same rules concerning form and termination as ordinary instance declarations,
2509 controlled by the same flags; see <xref linkend="instance-decls"/>.
2512 Unlike a <literal>deriving</literal>
2513 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2514 than the data type (assuming you also use
2515 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2518 data Foo a = Bar a | Baz String
2520 deriving instance Eq a => Eq (Foo [a])
2521 deriving instance Eq a => Eq (Foo (Maybe a))
2523 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2524 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2527 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2528 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2531 newtype Foo a = MkFoo (State Int a)
2533 deriving instance MonadState Int Foo
2535 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2536 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2542 <sect2 id="deriving-typeable">
2543 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2546 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2547 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2548 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2549 classes <literal>Eq</literal>, <literal>Ord</literal>,
2550 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2553 GHC extends this list with two more classes that may be automatically derived
2554 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2555 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2556 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2557 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2559 <para>An instance of <literal>Typeable</literal> can only be derived if the
2560 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2561 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2563 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2564 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2566 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2567 are used, and only <literal>Typeable1</literal> up to
2568 <literal>Typeable7</literal> are provided in the library.)
2569 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2570 class, whose kind suits that of the data type constructor, and
2571 then writing the data type instance by hand.
2575 <sect2 id="newtype-deriving">
2576 <title>Generalised derived instances for newtypes</title>
2579 When you define an abstract type using <literal>newtype</literal>, you may want
2580 the new type to inherit some instances from its representation. In
2581 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2582 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2583 other classes you have to write an explicit instance declaration. For
2584 example, if you define
2587 newtype Dollars = Dollars Int
2590 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2591 explicitly define an instance of <literal>Num</literal>:
2594 instance Num Dollars where
2595 Dollars a + Dollars b = Dollars (a+b)
2598 All the instance does is apply and remove the <literal>newtype</literal>
2599 constructor. It is particularly galling that, since the constructor
2600 doesn't appear at run-time, this instance declaration defines a
2601 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2602 dictionary, only slower!
2606 <sect3> <title> Generalising the deriving clause </title>
2608 GHC now permits such instances to be derived instead,
2609 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2612 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2615 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2616 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2617 derives an instance declaration of the form
2620 instance Num Int => Num Dollars
2623 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2627 We can also derive instances of constructor classes in a similar
2628 way. For example, suppose we have implemented state and failure monad
2629 transformers, such that
2632 instance Monad m => Monad (State s m)
2633 instance Monad m => Monad (Failure m)
2635 In Haskell 98, we can define a parsing monad by
2637 type Parser tok m a = State [tok] (Failure m) a
2640 which is automatically a monad thanks to the instance declarations
2641 above. With the extension, we can make the parser type abstract,
2642 without needing to write an instance of class <literal>Monad</literal>, via
2645 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2648 In this case the derived instance declaration is of the form
2650 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2653 Notice that, since <literal>Monad</literal> is a constructor class, the
2654 instance is a <emphasis>partial application</emphasis> of the new type, not the
2655 entire left hand side. We can imagine that the type declaration is
2656 "eta-converted" to generate the context of the instance
2661 We can even derive instances of multi-parameter classes, provided the
2662 newtype is the last class parameter. In this case, a ``partial
2663 application'' of the class appears in the <literal>deriving</literal>
2664 clause. For example, given the class
2667 class StateMonad s m | m -> s where ...
2668 instance Monad m => StateMonad s (State s m) where ...
2670 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2672 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2673 deriving (Monad, StateMonad [tok])
2676 The derived instance is obtained by completing the application of the
2677 class to the new type:
2680 instance StateMonad [tok] (State [tok] (Failure m)) =>
2681 StateMonad [tok] (Parser tok m)
2686 As a result of this extension, all derived instances in newtype
2687 declarations are treated uniformly (and implemented just by reusing
2688 the dictionary for the representation type), <emphasis>except</emphasis>
2689 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2690 the newtype and its representation.
2694 <sect3> <title> A more precise specification </title>
2696 Derived instance declarations are constructed as follows. Consider the
2697 declaration (after expansion of any type synonyms)
2700 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2706 The <literal>ci</literal> are partial applications of
2707 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2708 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2711 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2714 The type <literal>t</literal> is an arbitrary type.
2717 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2718 nor in the <literal>ci</literal>, and
2721 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2722 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2723 should not "look through" the type or its constructor. You can still
2724 derive these classes for a newtype, but it happens in the usual way, not
2725 via this new mechanism.
2728 Then, for each <literal>ci</literal>, the derived instance
2731 instance ci t => ci (T v1...vk)
2733 As an example which does <emphasis>not</emphasis> work, consider
2735 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2737 Here we cannot derive the instance
2739 instance Monad (State s m) => Monad (NonMonad m)
2742 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2743 and so cannot be "eta-converted" away. It is a good thing that this
2744 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2745 not, in fact, a monad --- for the same reason. Try defining
2746 <literal>>>=</literal> with the correct type: you won't be able to.
2750 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2751 important, since we can only derive instances for the last one. If the
2752 <literal>StateMonad</literal> class above were instead defined as
2755 class StateMonad m s | m -> s where ...
2758 then we would not have been able to derive an instance for the
2759 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2760 classes usually have one "main" parameter for which deriving new
2761 instances is most interesting.
2763 <para>Lastly, all of this applies only for classes other than
2764 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2765 and <literal>Data</literal>, for which the built-in derivation applies (section
2766 4.3.3. of the Haskell Report).
2767 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2768 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2769 the standard method is used or the one described here.)
2776 <!-- TYPE SYSTEM EXTENSIONS -->
2777 <sect1 id="type-class-extensions">
2778 <title>Class and instances declarations</title>
2780 <sect2 id="multi-param-type-classes">
2781 <title>Class declarations</title>
2784 This section, and the next one, documents GHC's type-class extensions.
2785 There's lots of background in the paper <ulink
2786 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2787 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2788 Jones, Erik Meijer).
2791 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2795 <title>Multi-parameter type classes</title>
2797 Multi-parameter type classes are permitted. For example:
2801 class Collection c a where
2802 union :: c a -> c a -> c a
2810 <title>The superclasses of a class declaration</title>
2813 There are no restrictions on the context in a class declaration
2814 (which introduces superclasses), except that the class hierarchy must
2815 be acyclic. So these class declarations are OK:
2819 class Functor (m k) => FiniteMap m k where
2822 class (Monad m, Monad (t m)) => Transform t m where
2823 lift :: m a -> (t m) a
2829 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2830 of "acyclic" involves only the superclass relationships. For example,
2836 op :: D b => a -> b -> b
2839 class C a => D a where { ... }
2843 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2844 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2845 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2852 <sect3 id="class-method-types">
2853 <title>Class method types</title>
2856 Haskell 98 prohibits class method types to mention constraints on the
2857 class type variable, thus:
2860 fromList :: [a] -> s a
2861 elem :: Eq a => a -> s a -> Bool
2863 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2864 contains the constraint <literal>Eq a</literal>, constrains only the
2865 class type variable (in this case <literal>a</literal>).
2866 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2873 <sect2 id="functional-dependencies">
2874 <title>Functional dependencies
2877 <para> Functional dependencies are implemented as described by Mark Jones
2878 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2879 In Proceedings of the 9th European Symposium on Programming,
2880 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2884 Functional dependencies are introduced by a vertical bar in the syntax of a
2885 class declaration; e.g.
2887 class (Monad m) => MonadState s m | m -> s where ...
2889 class Foo a b c | a b -> c where ...
2891 There should be more documentation, but there isn't (yet). Yell if you need it.
2894 <sect3><title>Rules for functional dependencies </title>
2896 In a class declaration, all of the class type variables must be reachable (in the sense
2897 mentioned in <xref linkend="type-restrictions"/>)
2898 from the free variables of each method type.
2902 class Coll s a where
2904 insert :: s -> a -> s
2907 is not OK, because the type of <literal>empty</literal> doesn't mention
2908 <literal>a</literal>. Functional dependencies can make the type variable
2911 class Coll s a | s -> a where
2913 insert :: s -> a -> s
2916 Alternatively <literal>Coll</literal> might be rewritten
2919 class Coll s a where
2921 insert :: s a -> a -> s a
2925 which makes the connection between the type of a collection of
2926 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2927 Occasionally this really doesn't work, in which case you can split the
2935 class CollE s => Coll s a where
2936 insert :: s -> a -> s
2943 <title>Background on functional dependencies</title>
2945 <para>The following description of the motivation and use of functional dependencies is taken
2946 from the Hugs user manual, reproduced here (with minor changes) by kind
2947 permission of Mark Jones.
2950 Consider the following class, intended as part of a
2951 library for collection types:
2953 class Collects e ce where
2955 insert :: e -> ce -> ce
2956 member :: e -> ce -> Bool
2958 The type variable e used here represents the element type, while ce is the type
2959 of the container itself. Within this framework, we might want to define
2960 instances of this class for lists or characteristic functions (both of which
2961 can be used to represent collections of any equality type), bit sets (which can
2962 be used to represent collections of characters), or hash tables (which can be
2963 used to represent any collection whose elements have a hash function). Omitting
2964 standard implementation details, this would lead to the following declarations:
2966 instance Eq e => Collects e [e] where ...
2967 instance Eq e => Collects e (e -> Bool) where ...
2968 instance Collects Char BitSet where ...
2969 instance (Hashable e, Collects a ce)
2970 => Collects e (Array Int ce) where ...
2972 All this looks quite promising; we have a class and a range of interesting
2973 implementations. Unfortunately, there are some serious problems with the class
2974 declaration. First, the empty function has an ambiguous type:
2976 empty :: Collects e ce => ce
2978 By "ambiguous" we mean that there is a type variable e that appears on the left
2979 of the <literal>=></literal> symbol, but not on the right. The problem with
2980 this is that, according to the theoretical foundations of Haskell overloading,
2981 we cannot guarantee a well-defined semantics for any term with an ambiguous
2985 We can sidestep this specific problem by removing the empty member from the
2986 class declaration. However, although the remaining members, insert and member,
2987 do not have ambiguous types, we still run into problems when we try to use
2988 them. For example, consider the following two functions:
2990 f x y = insert x . insert y
2993 for which GHC infers the following types:
2995 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2996 g :: (Collects Bool c, Collects Char c) => c -> c
2998 Notice that the type for f allows the two parameters x and y to be assigned
2999 different types, even though it attempts to insert each of the two values, one
3000 after the other, into the same collection. If we're trying to model collections
3001 that contain only one type of value, then this is clearly an inaccurate
3002 type. Worse still, the definition for g is accepted, without causing a type
3003 error. As a result, the error in this code will not be flagged at the point
3004 where it appears. Instead, it will show up only when we try to use g, which
3005 might even be in a different module.
3008 <sect4><title>An attempt to use constructor classes</title>
3011 Faced with the problems described above, some Haskell programmers might be
3012 tempted to use something like the following version of the class declaration:
3014 class Collects e c where
3016 insert :: e -> c e -> c e
3017 member :: e -> c e -> Bool
3019 The key difference here is that we abstract over the type constructor c that is
3020 used to form the collection type c e, and not over that collection type itself,
3021 represented by ce in the original class declaration. This avoids the immediate
3022 problems that we mentioned above: empty has type <literal>Collects e c => c
3023 e</literal>, which is not ambiguous.
3026 The function f from the previous section has a more accurate type:
3028 f :: (Collects e c) => e -> e -> c e -> c e
3030 The function g from the previous section is now rejected with a type error as
3031 we would hope because the type of f does not allow the two arguments to have
3033 This, then, is an example of a multiple parameter class that does actually work
3034 quite well in practice, without ambiguity problems.
3035 There is, however, a catch. This version of the Collects class is nowhere near
3036 as general as the original class seemed to be: only one of the four instances
3037 for <literal>Collects</literal>
3038 given above can be used with this version of Collects because only one of
3039 them---the instance for lists---has a collection type that can be written in
3040 the form c e, for some type constructor c, and element type e.
3044 <sect4><title>Adding functional dependencies</title>
3047 To get a more useful version of the Collects class, Hugs provides a mechanism
3048 that allows programmers to specify dependencies between the parameters of a
3049 multiple parameter class (For readers with an interest in theoretical
3050 foundations and previous work: The use of dependency information can be seen
3051 both as a generalization of the proposal for `parametric type classes' that was
3052 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3053 later framework for "improvement" of qualified types. The
3054 underlying ideas are also discussed in a more theoretical and abstract setting
3055 in a manuscript [implparam], where they are identified as one point in a
3056 general design space for systems of implicit parameterization.).
3058 To start with an abstract example, consider a declaration such as:
3060 class C a b where ...
3062 which tells us simply that C can be thought of as a binary relation on types
3063 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3064 included in the definition of classes to add information about dependencies
3065 between parameters, as in the following examples:
3067 class D a b | a -> b where ...
3068 class E a b | a -> b, b -> a where ...
3070 The notation <literal>a -> b</literal> used here between the | and where
3071 symbols --- not to be
3072 confused with a function type --- indicates that the a parameter uniquely
3073 determines the b parameter, and might be read as "a determines b." Thus D is
3074 not just a relation, but actually a (partial) function. Similarly, from the two
3075 dependencies that are included in the definition of E, we can see that E
3076 represents a (partial) one-one mapping between types.
3079 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3080 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3081 m>=0, meaning that the y parameters are uniquely determined by the x
3082 parameters. Spaces can be used as separators if more than one variable appears
3083 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3084 annotated with multiple dependencies using commas as separators, as in the
3085 definition of E above. Some dependencies that we can write in this notation are
3086 redundant, and will be rejected because they don't serve any useful
3087 purpose, and may instead indicate an error in the program. Examples of
3088 dependencies like this include <literal>a -> a </literal>,
3089 <literal>a -> a a </literal>,
3090 <literal>a -> </literal>, etc. There can also be
3091 some redundancy if multiple dependencies are given, as in
3092 <literal>a->b</literal>,
3093 <literal>b->c </literal>, <literal>a->c </literal>, and
3094 in which some subset implies the remaining dependencies. Examples like this are
3095 not treated as errors. Note that dependencies appear only in class
3096 declarations, and not in any other part of the language. In particular, the
3097 syntax for instance declarations, class constraints, and types is completely
3101 By including dependencies in a class declaration, we provide a mechanism for
3102 the programmer to specify each multiple parameter class more precisely. The
3103 compiler, on the other hand, is responsible for ensuring that the set of
3104 instances that are in scope at any given point in the program is consistent
3105 with any declared dependencies. For example, the following pair of instance
3106 declarations cannot appear together in the same scope because they violate the
3107 dependency for D, even though either one on its own would be acceptable:
3109 instance D Bool Int where ...
3110 instance D Bool Char where ...
3112 Note also that the following declaration is not allowed, even by itself:
3114 instance D [a] b where ...
3116 The problem here is that this instance would allow one particular choice of [a]
3117 to be associated with more than one choice for b, which contradicts the
3118 dependency specified in the definition of D. More generally, this means that,
3119 in any instance of the form:
3121 instance D t s where ...
3123 for some particular types t and s, the only variables that can appear in s are
3124 the ones that appear in t, and hence, if the type t is known, then s will be
3125 uniquely determined.
3128 The benefit of including dependency information is that it allows us to define
3129 more general multiple parameter classes, without ambiguity problems, and with
3130 the benefit of more accurate types. To illustrate this, we return to the
3131 collection class example, and annotate the original definition of <literal>Collects</literal>
3132 with a simple dependency:
3134 class Collects e ce | ce -> e where
3136 insert :: e -> ce -> ce
3137 member :: e -> ce -> Bool
3139 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3140 determined by the type of the collection ce. Note that both parameters of
3141 Collects are of kind *; there are no constructor classes here. Note too that
3142 all of the instances of Collects that we gave earlier can be used
3143 together with this new definition.
3146 What about the ambiguity problems that we encountered with the original
3147 definition? The empty function still has type Collects e ce => ce, but it is no
3148 longer necessary to regard that as an ambiguous type: Although the variable e
3149 does not appear on the right of the => symbol, the dependency for class
3150 Collects tells us that it is uniquely determined by ce, which does appear on
3151 the right of the => symbol. Hence the context in which empty is used can still
3152 give enough information to determine types for both ce and e, without
3153 ambiguity. More generally, we need only regard a type as ambiguous if it
3154 contains a variable on the left of the => that is not uniquely determined
3155 (either directly or indirectly) by the variables on the right.
3158 Dependencies also help to produce more accurate types for user defined
3159 functions, and hence to provide earlier detection of errors, and less cluttered
3160 types for programmers to work with. Recall the previous definition for a
3163 f x y = insert x y = insert x . insert y
3165 for which we originally obtained a type:
3167 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3169 Given the dependency information that we have for Collects, however, we can
3170 deduce that a and b must be equal because they both appear as the second
3171 parameter in a Collects constraint with the same first parameter c. Hence we
3172 can infer a shorter and more accurate type for f:
3174 f :: (Collects a c) => a -> a -> c -> c
3176 In a similar way, the earlier definition of g will now be flagged as a type error.
3179 Although we have given only a few examples here, it should be clear that the
3180 addition of dependency information can help to make multiple parameter classes
3181 more useful in practice, avoiding ambiguity problems, and allowing more general
3182 sets of instance declarations.
3188 <sect2 id="instance-decls">
3189 <title>Instance declarations</title>
3191 <sect3 id="instance-rules">
3192 <title>Relaxed rules for instance declarations</title>
3194 <para>An instance declaration has the form
3196 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 ...
3198 The part before the "<literal>=></literal>" is the
3199 <emphasis>context</emphasis>, while the part after the
3200 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3204 In Haskell 98 the head of an instance declaration
3205 must be of the form <literal>C (T a1 ... an)</literal>, where
3206 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3207 and the <literal>a1 ... an</literal> are distinct type variables.
3208 Furthermore, the assertions in the context of the instance declaration
3209 must be of the form <literal>C a</literal> where <literal>a</literal>
3210 is a type variable that occurs in the head.
3213 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3214 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3215 the context and head of the instance declaration can each consist of arbitrary
3216 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3220 The Paterson Conditions: for each assertion in the context
3222 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3223 <listitem><para>The assertion has fewer constructors and variables (taken together
3224 and counting repetitions) than the head</para></listitem>
3228 <listitem><para>The Coverage Condition. For each functional dependency,
3229 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3230 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3231 every type variable in
3232 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3233 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3234 substitution mapping each type variable in the class declaration to the
3235 corresponding type in the instance declaration.
3238 These restrictions ensure that context reduction terminates: each reduction
3239 step makes the problem smaller by at least one
3240 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3241 if you give the <option>-XUndecidableInstances</option>
3242 flag (<xref linkend="undecidable-instances"/>).
3243 You can find lots of background material about the reason for these
3244 restrictions in the paper <ulink
3245 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3246 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3249 For example, these are OK:
3251 instance C Int [a] -- Multiple parameters
3252 instance Eq (S [a]) -- Structured type in head
3254 -- Repeated type variable in head
3255 instance C4 a a => C4 [a] [a]
3256 instance Stateful (ST s) (MutVar s)
3258 -- Head can consist of type variables only
3260 instance (Eq a, Show b) => C2 a b
3262 -- Non-type variables in context
3263 instance Show (s a) => Show (Sized s a)
3264 instance C2 Int a => C3 Bool [a]
3265 instance C2 Int a => C3 [a] b
3269 -- Context assertion no smaller than head
3270 instance C a => C a where ...
3271 -- (C b b) has more more occurrences of b than the head
3272 instance C b b => Foo [b] where ...
3277 The same restrictions apply to instances generated by
3278 <literal>deriving</literal> clauses. Thus the following is accepted:
3280 data MinHeap h a = H a (h a)
3283 because the derived instance
3285 instance (Show a, Show (h a)) => Show (MinHeap h a)
3287 conforms to the above rules.
3291 A useful idiom permitted by the above rules is as follows.
3292 If one allows overlapping instance declarations then it's quite
3293 convenient to have a "default instance" declaration that applies if
3294 something more specific does not:
3302 <sect3 id="undecidable-instances">
3303 <title>Undecidable instances</title>
3306 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3307 For example, sometimes you might want to use the following to get the
3308 effect of a "class synonym":
3310 class (C1 a, C2 a, C3 a) => C a where { }
3312 instance (C1 a, C2 a, C3 a) => C a where { }
3314 This allows you to write shorter signatures:
3320 f :: (C1 a, C2 a, C3 a) => ...
3322 The restrictions on functional dependencies (<xref
3323 linkend="functional-dependencies"/>) are particularly troublesome.
3324 It is tempting to introduce type variables in the context that do not appear in
3325 the head, something that is excluded by the normal rules. For example:
3327 class HasConverter a b | a -> b where
3330 data Foo a = MkFoo a
3332 instance (HasConverter a b,Show b) => Show (Foo a) where
3333 show (MkFoo value) = show (convert value)
3335 This is dangerous territory, however. Here, for example, is a program that would make the
3340 instance F [a] [[a]]
3341 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3343 Similarly, it can be tempting to lift the coverage condition:
3345 class Mul a b c | a b -> c where
3346 (.*.) :: a -> b -> c
3348 instance Mul Int Int Int where (.*.) = (*)
3349 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3350 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3352 The third instance declaration does not obey the coverage condition;
3353 and indeed the (somewhat strange) definition:
3355 f = \ b x y -> if b then x .*. [y] else y
3357 makes instance inference go into a loop, because it requires the constraint
3358 <literal>(Mul a [b] b)</literal>.
3361 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3362 the experimental flag <option>-XUndecidableInstances</option>
3363 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3364 both the Paterson Conditions and the Coverage Condition
3365 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3366 fixed-depth recursion stack. If you exceed the stack depth you get a
3367 sort of backtrace, and the opportunity to increase the stack depth
3368 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3374 <sect3 id="instance-overlap">
3375 <title>Overlapping instances</title>
3377 In general, <emphasis>GHC requires that that it be unambiguous which instance
3379 should be used to resolve a type-class constraint</emphasis>. This behaviour
3380 can be modified by two flags: <option>-XOverlappingInstances</option>
3381 <indexterm><primary>-XOverlappingInstances
3382 </primary></indexterm>
3383 and <option>-XIncoherentInstances</option>
3384 <indexterm><primary>-XIncoherentInstances
3385 </primary></indexterm>, as this section discusses. Both these
3386 flags are dynamic flags, and can be set on a per-module basis, using
3387 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3389 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3390 it tries to match every instance declaration against the
3392 by instantiating the head of the instance declaration. For example, consider
3395 instance context1 => C Int a where ... -- (A)
3396 instance context2 => C a Bool where ... -- (B)
3397 instance context3 => C Int [a] where ... -- (C)
3398 instance context4 => C Int [Int] where ... -- (D)
3400 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3401 but (C) and (D) do not. When matching, GHC takes
3402 no account of the context of the instance declaration
3403 (<literal>context1</literal> etc).
3404 GHC's default behaviour is that <emphasis>exactly one instance must match the
3405 constraint it is trying to resolve</emphasis>.
3406 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3407 including both declarations (A) and (B), say); an error is only reported if a
3408 particular constraint matches more than one.
3412 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3413 more than one instance to match, provided there is a most specific one. For
3414 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3415 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3416 most-specific match, the program is rejected.
3419 However, GHC is conservative about committing to an overlapping instance. For example:
3424 Suppose that from the RHS of <literal>f</literal> we get the constraint
3425 <literal>C Int [b]</literal>. But
3426 GHC does not commit to instance (C), because in a particular
3427 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3428 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3429 So GHC rejects the program.
3430 (If you add the flag <option>-XIncoherentInstances</option>,
3431 GHC will instead pick (C), without complaining about
3432 the problem of subsequent instantiations.)
3435 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3436 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3437 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3438 it instead. In this case, GHC will refrain from
3439 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3440 as before) but, rather than rejecting the program, it will infer the type
3442 f :: C Int b => [b] -> [b]
3444 That postpones the question of which instance to pick to the
3445 call site for <literal>f</literal>
3446 by which time more is known about the type <literal>b</literal>.
3449 The willingness to be overlapped or incoherent is a property of
3450 the <emphasis>instance declaration</emphasis> itself, controlled by the
3451 presence or otherwise of the <option>-XOverlappingInstances</option>
3452 and <option>-XIncoherentInstances</option> flags when that module is
3453 being defined. Neither flag is required in a module that imports and uses the
3454 instance declaration. Specifically, during the lookup process:
3457 An instance declaration is ignored during the lookup process if (a) a more specific
3458 match is found, and (b) the instance declaration was compiled with
3459 <option>-XOverlappingInstances</option>. The flag setting for the
3460 more-specific instance does not matter.
3463 Suppose an instance declaration does not match the constraint being looked up, but
3464 does unify with it, so that it might match when the constraint is further
3465 instantiated. Usually GHC will regard this as a reason for not committing to
3466 some other constraint. But if the instance declaration was compiled with
3467 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3468 check for that declaration.
3471 These rules make it possible for a library author to design a library that relies on
3472 overlapping instances without the library client having to know.
3475 If an instance declaration is compiled without
3476 <option>-XOverlappingInstances</option>,
3477 then that instance can never be overlapped. This could perhaps be
3478 inconvenient. Perhaps the rule should instead say that the
3479 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3480 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3481 at a usage site should be permitted regardless of how the instance declarations
3482 are compiled, if the <option>-XOverlappingInstances</option> flag is
3483 used at the usage site. (Mind you, the exact usage site can occasionally be
3484 hard to pin down.) We are interested to receive feedback on these points.
3486 <para>The <option>-XIncoherentInstances</option> flag implies the
3487 <option>-XOverlappingInstances</option> flag, but not vice versa.
3492 <title>Type synonyms in the instance head</title>
3495 <emphasis>Unlike Haskell 98, instance heads may use type
3496 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3497 As always, using a type synonym is just shorthand for
3498 writing the RHS of the type synonym definition. For example:
3502 type Point = (Int,Int)
3503 instance C Point where ...
3504 instance C [Point] where ...
3508 is legal. However, if you added
3512 instance C (Int,Int) where ...
3516 as well, then the compiler will complain about the overlapping
3517 (actually, identical) instance declarations. As always, type synonyms
3518 must be fully applied. You cannot, for example, write:
3523 instance Monad P where ...
3527 This design decision is independent of all the others, and easily
3528 reversed, but it makes sense to me.
3536 <sect2 id="overloaded-strings">
3537 <title>Overloaded string literals
3541 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3542 string literal has type <literal>String</literal>, but with overloaded string
3543 literals enabled (with <literal>-XOverloadedStrings</literal>)
3544 a string literal has type <literal>(IsString a) => a</literal>.
3547 This means that the usual string syntax can be used, e.g., for packed strings
3548 and other variations of string like types. String literals behave very much
3549 like integer literals, i.e., they can be used in both expressions and patterns.
3550 If used in a pattern the literal with be replaced by an equality test, in the same
3551 way as an integer literal is.
3554 The class <literal>IsString</literal> is defined as:
3556 class IsString a where
3557 fromString :: String -> a
3559 The only predefined instance is the obvious one to make strings work as usual:
3561 instance IsString [Char] where
3564 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3565 it explicitly (for example, to give an instance declaration for it), you can import it
3566 from module <literal>GHC.Exts</literal>.
3569 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3573 Each type in a default declaration must be an
3574 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3578 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3579 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3580 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3581 <emphasis>or</emphasis> <literal>IsString</literal>.
3590 import GHC.Exts( IsString(..) )
3592 newtype MyString = MyString String deriving (Eq, Show)
3593 instance IsString MyString where
3594 fromString = MyString
3596 greet :: MyString -> MyString
3597 greet "hello" = "world"
3601 print $ greet "hello"
3602 print $ greet "fool"
3606 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3607 to work since it gets translated into an equality comparison.
3613 <sect1 id="other-type-extensions">
3614 <title>Other type system extensions</title>
3616 <sect2 id="type-restrictions">
3617 <title>Type signatures</title>
3619 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3621 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3622 the form <emphasis>(class type-variable)</emphasis> or
3623 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3624 these type signatures are perfectly OK
3627 g :: Ord (T a ()) => ...
3631 GHC imposes the following restrictions on the constraints in a type signature.
3635 forall tv1..tvn (c1, ...,cn) => type
3638 (Here, we write the "foralls" explicitly, although the Haskell source
3639 language omits them; in Haskell 98, all the free type variables of an
3640 explicit source-language type signature are universally quantified,
3641 except for the class type variables in a class declaration. However,
3642 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3651 <emphasis>Each universally quantified type variable
3652 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3654 A type variable <literal>a</literal> is "reachable" if it appears
3655 in the same constraint as either a type variable free in
3656 <literal>type</literal>, or another reachable type variable.
3657 A value with a type that does not obey
3658 this reachability restriction cannot be used without introducing
3659 ambiguity; that is why the type is rejected.
3660 Here, for example, is an illegal type:
3664 forall a. Eq a => Int
3668 When a value with this type was used, the constraint <literal>Eq tv</literal>
3669 would be introduced where <literal>tv</literal> is a fresh type variable, and
3670 (in the dictionary-translation implementation) the value would be
3671 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3672 can never know which instance of <literal>Eq</literal> to use because we never
3673 get any more information about <literal>tv</literal>.
3677 that the reachability condition is weaker than saying that <literal>a</literal> is
3678 functionally dependent on a type variable free in
3679 <literal>type</literal> (see <xref
3680 linkend="functional-dependencies"/>). The reason for this is there
3681 might be a "hidden" dependency, in a superclass perhaps. So
3682 "reachable" is a conservative approximation to "functionally dependent".
3683 For example, consider:
3685 class C a b | a -> b where ...
3686 class C a b => D a b where ...
3687 f :: forall a b. D a b => a -> a
3689 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3690 but that is not immediately apparent from <literal>f</literal>'s type.
3696 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3697 universally quantified type variables <literal>tvi</literal></emphasis>.
3699 For example, this type is OK because <literal>C a b</literal> mentions the
3700 universally quantified type variable <literal>b</literal>:
3704 forall a. C a b => burble
3708 The next type is illegal because the constraint <literal>Eq b</literal> does not
3709 mention <literal>a</literal>:
3713 forall a. Eq b => burble
3717 The reason for this restriction is milder than the other one. The
3718 excluded types are never useful or necessary (because the offending
3719 context doesn't need to be witnessed at this point; it can be floated
3720 out). Furthermore, floating them out increases sharing. Lastly,
3721 excluding them is a conservative choice; it leaves a patch of
3722 territory free in case we need it later.
3736 <sect2 id="implicit-parameters">
3737 <title>Implicit parameters</title>
3739 <para> Implicit parameters are implemented as described in
3740 "Implicit parameters: dynamic scoping with static types",
3741 J Lewis, MB Shields, E Meijer, J Launchbury,
3742 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3746 <para>(Most of the following, still rather incomplete, documentation is
3747 due to Jeff Lewis.)</para>
3749 <para>Implicit parameter support is enabled with the option
3750 <option>-XImplicitParams</option>.</para>
3753 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3754 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3755 context. In Haskell, all variables are statically bound. Dynamic
3756 binding of variables is a notion that goes back to Lisp, but was later
3757 discarded in more modern incarnations, such as Scheme. Dynamic binding
3758 can be very confusing in an untyped language, and unfortunately, typed
3759 languages, in particular Hindley-Milner typed languages like Haskell,
3760 only support static scoping of variables.
3763 However, by a simple extension to the type class system of Haskell, we
3764 can support dynamic binding. Basically, we express the use of a
3765 dynamically bound variable as a constraint on the type. These
3766 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3767 function uses a dynamically-bound variable <literal>?x</literal>
3768 of type <literal>t'</literal>". For
3769 example, the following expresses the type of a sort function,
3770 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3772 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3774 The dynamic binding constraints are just a new form of predicate in the type class system.
3777 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3778 where <literal>x</literal> is
3779 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3780 Use of this construct also introduces a new
3781 dynamic-binding constraint in the type of the expression.
3782 For example, the following definition
3783 shows how we can define an implicitly parameterized sort function in
3784 terms of an explicitly parameterized <literal>sortBy</literal> function:
3786 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3788 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3794 <title>Implicit-parameter type constraints</title>
3796 Dynamic binding constraints behave just like other type class
3797 constraints in that they are automatically propagated. Thus, when a
3798 function is used, its implicit parameters are inherited by the
3799 function that called it. For example, our <literal>sort</literal> function might be used
3800 to pick out the least value in a list:
3802 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3803 least xs = head (sort xs)
3805 Without lifting a finger, the <literal>?cmp</literal> parameter is
3806 propagated to become a parameter of <literal>least</literal> as well. With explicit
3807 parameters, the default is that parameters must always be explicit
3808 propagated. With implicit parameters, the default is to always
3812 An implicit-parameter type constraint differs from other type class constraints in the
3813 following way: All uses of a particular implicit parameter must have
3814 the same type. This means that the type of <literal>(?x, ?x)</literal>
3815 is <literal>(?x::a) => (a,a)</literal>, and not
3816 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3820 <para> You can't have an implicit parameter in the context of a class or instance
3821 declaration. For example, both these declarations are illegal:
3823 class (?x::Int) => C a where ...
3824 instance (?x::a) => Foo [a] where ...
3826 Reason: exactly which implicit parameter you pick up depends on exactly where
3827 you invoke a function. But the ``invocation'' of instance declarations is done
3828 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3829 Easiest thing is to outlaw the offending types.</para>
3831 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3833 f :: (?x :: [a]) => Int -> Int
3836 g :: (Read a, Show a) => String -> String
3839 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3840 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3841 quite unambiguous, and fixes the type <literal>a</literal>.
3846 <title>Implicit-parameter bindings</title>
3849 An implicit parameter is <emphasis>bound</emphasis> using the standard
3850 <literal>let</literal> or <literal>where</literal> binding forms.
3851 For example, we define the <literal>min</literal> function by binding
3852 <literal>cmp</literal>.
3855 min = let ?cmp = (<=) in least
3859 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3860 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3861 (including in a list comprehension, or do-notation, or pattern guards),
3862 or a <literal>where</literal> clause.
3863 Note the following points:
3866 An implicit-parameter binding group must be a
3867 collection of simple bindings to implicit-style variables (no
3868 function-style bindings, and no type signatures); these bindings are
3869 neither polymorphic or recursive.
3872 You may not mix implicit-parameter bindings with ordinary bindings in a
3873 single <literal>let</literal>
3874 expression; use two nested <literal>let</literal>s instead.
3875 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3879 You may put multiple implicit-parameter bindings in a
3880 single binding group; but they are <emphasis>not</emphasis> treated
3881 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3882 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3883 parameter. The bindings are not nested, and may be re-ordered without changing
3884 the meaning of the program.
3885 For example, consider:
3887 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3889 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3890 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3892 f :: (?x::Int) => Int -> Int
3900 <sect3><title>Implicit parameters and polymorphic recursion</title>
3903 Consider these two definitions:
3906 len1 xs = let ?acc = 0 in len_acc1 xs
3909 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3914 len2 xs = let ?acc = 0 in len_acc2 xs
3916 len_acc2 :: (?acc :: Int) => [a] -> Int
3918 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3920 The only difference between the two groups is that in the second group
3921 <literal>len_acc</literal> is given a type signature.
3922 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3923 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3924 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3925 has a type signature, the recursive call is made to the
3926 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
3927 as an implicit parameter. So we get the following results in GHCi:
3934 Adding a type signature dramatically changes the result! This is a rather
3935 counter-intuitive phenomenon, worth watching out for.
3939 <sect3><title>Implicit parameters and monomorphism</title>
3941 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3942 Haskell Report) to implicit parameters. For example, consider:
3950 Since the binding for <literal>y</literal> falls under the Monomorphism
3951 Restriction it is not generalised, so the type of <literal>y</literal> is
3952 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3953 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3954 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3955 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3956 <literal>y</literal> in the body of the <literal>let</literal> will see the
3957 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3958 <literal>14</literal>.
3963 <!-- ======================= COMMENTED OUT ========================
3965 We intend to remove linear implicit parameters, so I'm at least removing
3966 them from the 6.6 user manual
3968 <sect2 id="linear-implicit-parameters">
3969 <title>Linear implicit parameters</title>
3971 Linear implicit parameters are an idea developed by Koen Claessen,
3972 Mark Shields, and Simon PJ. They address the long-standing
3973 problem that monads seem over-kill for certain sorts of problem, notably:
3976 <listitem> <para> distributing a supply of unique names </para> </listitem>
3977 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3978 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3982 Linear implicit parameters are just like ordinary implicit parameters,
3983 except that they are "linear"; that is, they cannot be copied, and
3984 must be explicitly "split" instead. Linear implicit parameters are
3985 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3986 (The '/' in the '%' suggests the split!)
3991 import GHC.Exts( Splittable )
3993 data NameSupply = ...
3995 splitNS :: NameSupply -> (NameSupply, NameSupply)
3996 newName :: NameSupply -> Name
3998 instance Splittable NameSupply where
4002 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4003 f env (Lam x e) = Lam x' (f env e)
4006 env' = extend env x x'
4007 ...more equations for f...
4009 Notice that the implicit parameter %ns is consumed
4011 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4012 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4016 So the translation done by the type checker makes
4017 the parameter explicit:
4019 f :: NameSupply -> Env -> Expr -> Expr
4020 f ns env (Lam x e) = Lam x' (f ns1 env e)
4022 (ns1,ns2) = splitNS ns
4024 env = extend env x x'
4026 Notice the call to 'split' introduced by the type checker.
4027 How did it know to use 'splitNS'? Because what it really did
4028 was to introduce a call to the overloaded function 'split',
4029 defined by the class <literal>Splittable</literal>:
4031 class Splittable a where
4034 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4035 split for name supplies. But we can simply write
4041 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4043 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4044 <literal>GHC.Exts</literal>.
4049 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4050 are entirely distinct implicit parameters: you
4051 can use them together and they won't interfere with each other. </para>
4054 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4056 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4057 in the context of a class or instance declaration. </para></listitem>
4061 <sect3><title>Warnings</title>
4064 The monomorphism restriction is even more important than usual.
4065 Consider the example above:
4067 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4068 f env (Lam x e) = Lam x' (f env e)
4071 env' = extend env x x'
4073 If we replaced the two occurrences of x' by (newName %ns), which is
4074 usually a harmless thing to do, we get:
4076 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4077 f env (Lam x e) = Lam (newName %ns) (f env e)
4079 env' = extend env x (newName %ns)
4081 But now the name supply is consumed in <emphasis>three</emphasis> places
4082 (the two calls to newName,and the recursive call to f), so
4083 the result is utterly different. Urk! We don't even have
4087 Well, this is an experimental change. With implicit
4088 parameters we have already lost beta reduction anyway, and
4089 (as John Launchbury puts it) we can't sensibly reason about
4090 Haskell programs without knowing their typing.
4095 <sect3><title>Recursive functions</title>
4096 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4099 foo :: %x::T => Int -> [Int]
4101 foo n = %x : foo (n-1)
4103 where T is some type in class Splittable.</para>
4105 Do you get a list of all the same T's or all different T's
4106 (assuming that split gives two distinct T's back)?
4108 If you supply the type signature, taking advantage of polymorphic
4109 recursion, you get what you'd probably expect. Here's the
4110 translated term, where the implicit param is made explicit:
4113 foo x n = let (x1,x2) = split x
4114 in x1 : foo x2 (n-1)
4116 But if you don't supply a type signature, GHC uses the Hindley
4117 Milner trick of using a single monomorphic instance of the function
4118 for the recursive calls. That is what makes Hindley Milner type inference
4119 work. So the translation becomes
4123 foom n = x : foom (n-1)
4127 Result: 'x' is not split, and you get a list of identical T's. So the
4128 semantics of the program depends on whether or not foo has a type signature.
4131 You may say that this is a good reason to dislike linear implicit parameters
4132 and you'd be right. That is why they are an experimental feature.
4138 ================ END OF Linear Implicit Parameters commented out -->
4140 <sect2 id="kinding">
4141 <title>Explicitly-kinded quantification</title>
4144 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4145 to give the kind explicitly as (machine-checked) documentation,
4146 just as it is nice to give a type signature for a function. On some occasions,
4147 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4148 John Hughes had to define the data type:
4150 data Set cxt a = Set [a]
4151 | Unused (cxt a -> ())
4153 The only use for the <literal>Unused</literal> constructor was to force the correct
4154 kind for the type variable <literal>cxt</literal>.
4157 GHC now instead allows you to specify the kind of a type variable directly, wherever
4158 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4161 This flag enables kind signatures in the following places:
4163 <listitem><para><literal>data</literal> declarations:
4165 data Set (cxt :: * -> *) a = Set [a]
4166 </screen></para></listitem>
4167 <listitem><para><literal>type</literal> declarations:
4169 type T (f :: * -> *) = f Int
4170 </screen></para></listitem>
4171 <listitem><para><literal>class</literal> declarations:
4173 class (Eq a) => C (f :: * -> *) a where ...
4174 </screen></para></listitem>
4175 <listitem><para><literal>forall</literal>'s in type signatures:
4177 f :: forall (cxt :: * -> *). Set cxt Int
4178 </screen></para></listitem>
4183 The parentheses are required. Some of the spaces are required too, to
4184 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4185 will get a parse error, because "<literal>::*->*</literal>" is a
4186 single lexeme in Haskell.
4190 As part of the same extension, you can put kind annotations in types
4193 f :: (Int :: *) -> Int
4194 g :: forall a. a -> (a :: *)
4198 atype ::= '(' ctype '::' kind ')
4200 The parentheses are required.
4205 <sect2 id="universal-quantification">
4206 <title>Arbitrary-rank polymorphism
4210 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4211 allows us to say exactly what this means. For example:
4219 g :: forall b. (b -> b)
4221 The two are treated identically.
4225 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4226 explicit universal quantification in
4228 For example, all the following types are legal:
4230 f1 :: forall a b. a -> b -> a
4231 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4233 f2 :: (forall a. a->a) -> Int -> Int
4234 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4236 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4238 f4 :: Int -> (forall a. a -> a)
4240 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4241 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4242 The <literal>forall</literal> makes explicit the universal quantification that
4243 is implicitly added by Haskell.
4246 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4247 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4248 shows, the polymorphic type on the left of the function arrow can be overloaded.
4251 The function <literal>f3</literal> has a rank-3 type;
4252 it has rank-2 types on the left of a function arrow.
4255 GHC has three flags to control higher-rank types:
4258 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4261 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4264 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4265 That is, you can nest <literal>forall</literal>s
4266 arbitrarily deep in function arrows.
4267 In particular, a forall-type (also called a "type scheme"),
4268 including an operational type class context, is legal:
4270 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4271 of a function arrow </para> </listitem>
4272 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4273 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4274 field type signatures.</para> </listitem>
4275 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4276 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4280 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4281 a type variable any more!
4290 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4291 the types of the constructor arguments. Here are several examples:
4297 data T a = T1 (forall b. b -> b -> b) a
4299 data MonadT m = MkMonad { return :: forall a. a -> m a,
4300 bind :: forall a b. m a -> (a -> m b) -> m b
4303 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4309 The constructors have rank-2 types:
4315 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4316 MkMonad :: forall m. (forall a. a -> m a)
4317 -> (forall a b. m a -> (a -> m b) -> m b)
4319 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4325 Notice that you don't need to use a <literal>forall</literal> if there's an
4326 explicit context. For example in the first argument of the
4327 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4328 prefixed to the argument type. The implicit <literal>forall</literal>
4329 quantifies all type variables that are not already in scope, and are
4330 mentioned in the type quantified over.
4334 As for type signatures, implicit quantification happens for non-overloaded
4335 types too. So if you write this:
4338 data T a = MkT (Either a b) (b -> b)
4341 it's just as if you had written this:
4344 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4347 That is, since the type variable <literal>b</literal> isn't in scope, it's
4348 implicitly universally quantified. (Arguably, it would be better
4349 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4350 where that is what is wanted. Feedback welcomed.)
4354 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4355 the constructor to suitable values, just as usual. For example,
4366 a3 = MkSwizzle reverse
4369 a4 = let r x = Just x
4376 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4377 mkTs f x y = [T1 f x, T1 f y]
4383 The type of the argument can, as usual, be more general than the type
4384 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4385 does not need the <literal>Ord</literal> constraint.)
4389 When you use pattern matching, the bound variables may now have
4390 polymorphic types. For example:
4396 f :: T a -> a -> (a, Char)
4397 f (T1 w k) x = (w k x, w 'c' 'd')
4399 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4400 g (MkSwizzle s) xs f = s (map f (s xs))
4402 h :: MonadT m -> [m a] -> m [a]
4403 h m [] = return m []
4404 h m (x:xs) = bind m x $ \y ->
4405 bind m (h m xs) $ \ys ->
4412 In the function <function>h</function> we use the record selectors <literal>return</literal>
4413 and <literal>bind</literal> to extract the polymorphic bind and return functions
4414 from the <literal>MonadT</literal> data structure, rather than using pattern
4420 <title>Type inference</title>
4423 In general, type inference for arbitrary-rank types is undecidable.
4424 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4425 to get a decidable algorithm by requiring some help from the programmer.
4426 We do not yet have a formal specification of "some help" but the rule is this:
4429 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4430 provides an explicit polymorphic type for x, or GHC's type inference will assume
4431 that x's type has no foralls in it</emphasis>.
4434 What does it mean to "provide" an explicit type for x? You can do that by
4435 giving a type signature for x directly, using a pattern type signature
4436 (<xref linkend="scoped-type-variables"/>), thus:
4438 \ f :: (forall a. a->a) -> (f True, f 'c')
4440 Alternatively, you can give a type signature to the enclosing
4441 context, which GHC can "push down" to find the type for the variable:
4443 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4445 Here the type signature on the expression can be pushed inwards
4446 to give a type signature for f. Similarly, and more commonly,
4447 one can give a type signature for the function itself:
4449 h :: (forall a. a->a) -> (Bool,Char)
4450 h f = (f True, f 'c')
4452 You don't need to give a type signature if the lambda bound variable
4453 is a constructor argument. Here is an example we saw earlier:
4455 f :: T a -> a -> (a, Char)
4456 f (T1 w k) x = (w k x, w 'c' 'd')
4458 Here we do not need to give a type signature to <literal>w</literal>, because
4459 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4466 <sect3 id="implicit-quant">
4467 <title>Implicit quantification</title>
4470 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4471 user-written types, if and only if there is no explicit <literal>forall</literal>,
4472 GHC finds all the type variables mentioned in the type that are not already
4473 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4477 f :: forall a. a -> a
4484 h :: forall b. a -> b -> b
4490 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4493 f :: (a -> a) -> Int
4495 f :: forall a. (a -> a) -> Int
4497 f :: (forall a. a -> a) -> Int
4500 g :: (Ord a => a -> a) -> Int
4501 -- MEANS the illegal type
4502 g :: forall a. (Ord a => a -> a) -> Int
4504 g :: (forall a. Ord a => a -> a) -> Int
4506 The latter produces an illegal type, which you might think is silly,
4507 but at least the rule is simple. If you want the latter type, you
4508 can write your for-alls explicitly. Indeed, doing so is strongly advised
4515 <sect2 id="impredicative-polymorphism">
4516 <title>Impredicative polymorphism
4518 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4519 enabled with <option>-XImpredicativeTypes</option>.
4521 that you can call a polymorphic function at a polymorphic type, and
4522 parameterise data structures over polymorphic types. For example:
4524 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4525 f (Just g) = Just (g [3], g "hello")
4528 Notice here that the <literal>Maybe</literal> type is parameterised by the
4529 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4532 <para>The technical details of this extension are described in the paper
4533 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4534 type inference for higher-rank types and impredicativity</ulink>,
4535 which appeared at ICFP 2006.
4539 <sect2 id="scoped-type-variables">
4540 <title>Lexically scoped type variables
4544 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4545 which some type signatures are simply impossible to write. For example:
4547 f :: forall a. [a] -> [a]
4553 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4554 the entire definition of <literal>f</literal>.
4555 In particular, it is in scope at the type signature for <varname>ys</varname>.
4556 In Haskell 98 it is not possible to declare
4557 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4558 it becomes possible to do so.
4560 <para>Lexically-scoped type variables are enabled by
4561 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4563 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4564 variables work, compared to earlier releases. Read this section
4568 <title>Overview</title>
4570 <para>The design follows the following principles
4572 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4573 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4574 design.)</para></listitem>
4575 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4576 type variables. This means that every programmer-written type signature
4577 (including one that contains free scoped type variables) denotes a
4578 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4579 checker, and no inference is involved.</para></listitem>
4580 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4581 changing the program.</para></listitem>
4585 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4587 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4588 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4589 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4590 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4594 In Haskell, a programmer-written type signature is implicitly quantified over
4595 its free type variables (<ulink
4596 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4598 of the Haskell Report).
4599 Lexically scoped type variables affect this implicit quantification rules
4600 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4601 quantified. For example, if type variable <literal>a</literal> is in scope,
4604 (e :: a -> a) means (e :: a -> a)
4605 (e :: b -> b) means (e :: forall b. b->b)
4606 (e :: a -> b) means (e :: forall b. a->b)
4614 <sect3 id="decl-type-sigs">
4615 <title>Declaration type signatures</title>
4616 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4617 quantification (using <literal>forall</literal>) brings into scope the
4618 explicitly-quantified
4619 type variables, in the definition of the named function. For example:
4621 f :: forall a. [a] -> [a]
4622 f (x:xs) = xs ++ [ x :: a ]
4624 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4625 the definition of "<literal>f</literal>".
4627 <para>This only happens if:
4629 <listitem><para> The quantification in <literal>f</literal>'s type
4630 signature is explicit. For example:
4633 g (x:xs) = xs ++ [ x :: a ]
4635 This program will be rejected, because "<literal>a</literal>" does not scope
4636 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4637 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4638 quantification rules.
4640 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4641 not a pattern binding.
4644 f1 :: forall a. [a] -> [a]
4645 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4647 f2 :: forall a. [a] -> [a]
4648 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4650 f3 :: forall a. [a] -> [a]
4651 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4653 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4654 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4655 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4656 the type signature brings <literal>a</literal> into scope.
4662 <sect3 id="exp-type-sigs">
4663 <title>Expression type signatures</title>
4665 <para>An expression type signature that has <emphasis>explicit</emphasis>
4666 quantification (using <literal>forall</literal>) brings into scope the
4667 explicitly-quantified
4668 type variables, in the annotated expression. For example:
4670 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4672 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4673 type variable <literal>s</literal> into scope, in the annotated expression
4674 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4679 <sect3 id="pattern-type-sigs">
4680 <title>Pattern type signatures</title>
4682 A type signature may occur in any pattern; this is a <emphasis>pattern type
4683 signature</emphasis>.
4686 -- f and g assume that 'a' is already in scope
4687 f = \(x::Int, y::a) -> x
4689 h ((x,y) :: (Int,Bool)) = (y,x)
4691 In the case where all the type variables in the pattern type signature are
4692 already in scope (i.e. bound by the enclosing context), matters are simple: the
4693 signature simply constrains the type of the pattern in the obvious way.
4696 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4697 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4698 that are already in scope. For example:
4700 f :: forall a. [a] -> (Int, [a])
4703 (ys::[a], n) = (reverse xs, length xs) -- OK
4704 zs::[a] = xs ++ ys -- OK
4706 Just (v::b) = ... -- Not OK; b is not in scope
4708 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4709 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4713 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4714 type signature may mention a type variable that is not in scope; in this case,
4715 <emphasis>the signature brings that type variable into scope</emphasis>.
4716 This is particularly important for existential data constructors. For example:
4718 data T = forall a. MkT [a]
4721 k (MkT [t::a]) = MkT t3
4725 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4726 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4727 because it is bound by the pattern match. GHC's rule is that in this situation
4728 (and only then), a pattern type signature can mention a type variable that is
4729 not already in scope; the effect is to bring it into scope, standing for the
4730 existentially-bound type variable.
4733 When a pattern type signature binds a type variable in this way, GHC insists that the
4734 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4735 This means that any user-written type signature always stands for a completely known type.
4738 If all this seems a little odd, we think so too. But we must have
4739 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4740 could not name existentially-bound type variables in subsequent type signatures.
4743 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4744 signature is allowed to mention a lexical variable that is not already in
4746 For example, both <literal>f</literal> and <literal>g</literal> would be
4747 illegal if <literal>a</literal> was not already in scope.
4753 <!-- ==================== Commented out part about result type signatures
4755 <sect3 id="result-type-sigs">
4756 <title>Result type signatures</title>
4759 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4762 {- f assumes that 'a' is already in scope -}
4763 f x y :: [a] = [x,y,x]
4765 g = \ x :: [Int] -> [3,4]
4767 h :: forall a. [a] -> a
4771 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4772 the result of the function. Similarly, the body of the lambda in the RHS of
4773 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4774 alternative in <literal>h</literal> is <literal>a</literal>.
4776 <para> A result type signature never brings new type variables into scope.</para>
4778 There are a couple of syntactic wrinkles. First, notice that all three
4779 examples would parse quite differently with parentheses:
4781 {- f assumes that 'a' is already in scope -}
4782 f x (y :: [a]) = [x,y,x]
4784 g = \ (x :: [Int]) -> [3,4]
4786 h :: forall a. [a] -> a
4790 Now the signature is on the <emphasis>pattern</emphasis>; and
4791 <literal>h</literal> would certainly be ill-typed (since the pattern
4792 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4794 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4795 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4796 token or a parenthesised type of some sort). To see why,
4797 consider how one would parse this:
4806 <sect3 id="cls-inst-scoped-tyvars">
4807 <title>Class and instance declarations</title>
4810 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4811 scope over the methods defined in the <literal>where</literal> part. For example:
4829 <sect2 id="typing-binds">
4830 <title>Generalised typing of mutually recursive bindings</title>
4833 The Haskell Report specifies that a group of bindings (at top level, or in a
4834 <literal>let</literal> or <literal>where</literal>) should be sorted into
4835 strongly-connected components, and then type-checked in dependency order
4836 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4837 Report, Section 4.5.1</ulink>).
4838 As each group is type-checked, any binders of the group that
4840 an explicit type signature are put in the type environment with the specified
4842 and all others are monomorphic until the group is generalised
4843 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4846 <para>Following a suggestion of Mark Jones, in his paper
4847 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4849 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4851 <emphasis>the dependency analysis ignores references to variables that have an explicit
4852 type signature</emphasis>.
4853 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4854 typecheck. For example, consider:
4856 f :: Eq a => a -> Bool
4857 f x = (x == x) || g True || g "Yes"
4859 g y = (y <= y) || f True
4861 This is rejected by Haskell 98, but under Jones's scheme the definition for
4862 <literal>g</literal> is typechecked first, separately from that for
4863 <literal>f</literal>,
4864 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4865 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4866 type is generalised, to get
4868 g :: Ord a => a -> Bool
4870 Now, the definition for <literal>f</literal> is typechecked, with this type for
4871 <literal>g</literal> in the type environment.
4875 The same refined dependency analysis also allows the type signatures of
4876 mutually-recursive functions to have different contexts, something that is illegal in
4877 Haskell 98 (Section 4.5.2, last sentence). With
4878 <option>-XRelaxedPolyRec</option>
4879 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4880 type signatures; in practice this means that only variables bound by the same
4881 pattern binding must have the same context. For example, this is fine:
4883 f :: Eq a => a -> Bool
4884 f x = (x == x) || g True
4886 g :: Ord a => a -> Bool
4887 g y = (y <= y) || f True
4892 <sect2 id="type-families">
4893 <title>Type families
4897 GHC supports the definition of type families indexed by types. They may be
4898 seen as an extension of Haskell 98's class-based overloading of values to
4899 types. When type families are declared in classes, they are also known as
4903 There are two forms of type families: data families and type synonym families.
4904 Currently, only the former are fully implemented, while we are still working
4905 on the latter. As a result, the specification of the language extension is
4906 also still to some degree in flux. Hence, a more detailed description of
4907 the language extension and its use is currently available
4908 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4909 wiki page on type families</ulink>. The material will be moved to this user's
4910 guide when it has stabilised.
4913 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4920 <!-- ==================== End of type system extensions ================= -->
4922 <!-- ====================== TEMPLATE HASKELL ======================= -->
4924 <sect1 id="template-haskell">
4925 <title>Template Haskell</title>
4927 <para>Template Haskell allows you to do compile-time meta-programming in
4930 the main technical innovations is discussed in "<ulink
4931 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
4932 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4935 There is a Wiki page about
4936 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
4937 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
4941 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4942 Haskell library reference material</ulink>
4943 (look for module <literal>Language.Haskell.TH</literal>).
4944 Many changes to the original design are described in
4945 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
4946 Notes on Template Haskell version 2</ulink>.
4947 Not all of these changes are in GHC, however.
4950 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
4951 as a worked example to help get you started.
4955 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
4956 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4961 <title>Syntax</title>
4963 <para> Template Haskell has the following new syntactic
4964 constructions. You need to use the flag
4965 <option>-XTemplateHaskell</option>
4966 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4967 </indexterm>to switch these syntactic extensions on
4968 (<option>-XTemplateHaskell</option> is no longer implied by
4969 <option>-fglasgow-exts</option>).</para>
4973 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4974 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4975 There must be no space between the "$" and the identifier or parenthesis. This use
4976 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4977 of "." as an infix operator. If you want the infix operator, put spaces around it.
4979 <para> A splice can occur in place of
4981 <listitem><para> an expression; the spliced expression must
4982 have type <literal>Q Exp</literal></para></listitem>
4983 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4986 Inside a splice you can can only call functions defined in imported modules,
4987 not functions defined elsewhere in the same module.</listitem>
4991 A expression quotation is written in Oxford brackets, thus:
4993 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4994 the quotation has type <literal>Q Exp</literal>.</para></listitem>
4995 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4996 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4997 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4998 the quotation has type <literal>Q Typ</literal>.</para></listitem>
4999 </itemizedlist></para></listitem>
5002 A quasi-quotation can appear in either a pattern context or an
5003 expression context and is also written in Oxford brackets:
5005 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5006 where the "..." is an arbitrary string; a full description of the
5007 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5008 </itemizedlist></para></listitem>
5011 A name can be quoted with either one or two prefix single quotes:
5013 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5014 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5015 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5017 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5018 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5021 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5022 may also be given as an argument to the <literal>reify</literal> function.
5028 (Compared to the original paper, there are many differences of detail.
5029 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5030 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5031 Type splices are not implemented, and neither are pattern splices or quotations.
5035 <sect2> <title> Using Template Haskell </title>
5039 The data types and monadic constructor functions for Template Haskell are in the library
5040 <literal>Language.Haskell.THSyntax</literal>.
5044 You can only run a function at compile time if it is imported from another module. That is,
5045 you can't define a function in a module, and call it from within a splice in the same module.
5046 (It would make sense to do so, but it's hard to implement.)
5050 You can only run a function at compile time if it is imported
5051 from another module <emphasis>that is not part of a mutually-recursive group of modules
5052 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5053 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5054 splice is to be run.</para>
5056 For example, when compiling module A,
5057 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5058 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5062 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5065 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5066 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5067 compiles and runs a program, and then looks at the result. So it's important that
5068 the program it compiles produces results whose representations are identical to
5069 those of the compiler itself.
5073 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5074 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5079 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5080 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5081 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5088 -- Import our template "pr"
5089 import Printf ( pr )
5091 -- The splice operator $ takes the Haskell source code
5092 -- generated at compile time by "pr" and splices it into
5093 -- the argument of "putStrLn".
5094 main = putStrLn ( $(pr "Hello") )
5100 -- Skeletal printf from the paper.
5101 -- It needs to be in a separate module to the one where
5102 -- you intend to use it.
5104 -- Import some Template Haskell syntax
5105 import Language.Haskell.TH
5107 -- Describe a format string
5108 data Format = D | S | L String
5110 -- Parse a format string. This is left largely to you
5111 -- as we are here interested in building our first ever
5112 -- Template Haskell program and not in building printf.
5113 parse :: String -> [Format]
5116 -- Generate Haskell source code from a parsed representation
5117 -- of the format string. This code will be spliced into
5118 -- the module which calls "pr", at compile time.
5119 gen :: [Format] -> Q Exp
5120 gen [D] = [| \n -> show n |]
5121 gen [S] = [| \s -> s |]
5122 gen [L s] = stringE s
5124 -- Here we generate the Haskell code for the splice
5125 -- from an input format string.
5126 pr :: String -> Q Exp
5127 pr s = gen (parse s)
5130 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5133 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5136 <para>Run "main.exe" and here is your output:</para>
5146 <title>Using Template Haskell with Profiling</title>
5147 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5149 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5150 interpreter to run the splice expressions. The bytecode interpreter
5151 runs the compiled expression on top of the same runtime on which GHC
5152 itself is running; this means that the compiled code referred to by
5153 the interpreted expression must be compatible with this runtime, and
5154 in particular this means that object code that is compiled for
5155 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5156 expression, because profiled object code is only compatible with the
5157 profiling version of the runtime.</para>
5159 <para>This causes difficulties if you have a multi-module program
5160 containing Template Haskell code and you need to compile it for
5161 profiling, because GHC cannot load the profiled object code and use it
5162 when executing the splices. Fortunately GHC provides a workaround.
5163 The basic idea is to compile the program twice:</para>
5167 <para>Compile the program or library first the normal way, without
5168 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5171 <para>Then compile it again with <option>-prof</option>, and
5172 additionally use <option>-osuf
5173 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5174 to name the object files differently (you can choose any suffix
5175 that isn't the normal object suffix here). GHC will automatically
5176 load the object files built in the first step when executing splice
5177 expressions. If you omit the <option>-osuf</option> flag when
5178 building with <option>-prof</option> and Template Haskell is used,
5179 GHC will emit an error message. </para>
5184 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5185 <para>Quasi-quotation allows patterns and expressions to be written using
5186 programmer-defined concrete syntax; the motivation behind the extension and
5187 several examples are documented in
5188 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5189 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5190 2007). The example below shows how to write a quasiquoter for a simple
5191 expression language.</para>
5194 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5195 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5196 functions for quoting expressions and patterns, respectively. The first argument
5197 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5198 context of the quasi-quotation statement determines which of the two parsers is
5199 called: if the quasi-quotation occurs in an expression context, the expression
5200 parser is called, and if it occurs in a pattern context, the pattern parser is
5204 Note that in the example we make use of an antiquoted
5205 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5206 (this syntax for anti-quotation was defined by the parser's
5207 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5208 integer value argument of the constructor <literal>IntExpr</literal> when
5209 pattern matching. Please see the referenced paper for further details regarding
5210 anti-quotation as well as the description of a technique that uses SYB to
5211 leverage a single parser of type <literal>String -> a</literal> to generate both
5212 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5213 pattern parser that returns a value of type <literal>Q Pat</literal>.
5216 <para>In general, a quasi-quote has the form
5217 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5218 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5219 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5220 can be arbitrary, and may contain newlines.
5223 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5224 the example, <literal>expr</literal> cannot be defined
5225 in <literal>Main.hs</literal> where it is used, but must be imported.
5236 main = do { print $ eval [$expr|1 + 2|]
5238 { [$expr|'int:n|] -> print n
5247 import qualified Language.Haskell.TH as TH
5248 import Language.Haskell.TH.Quasi
5250 data Expr = IntExpr Integer
5251 | AntiIntExpr String
5252 | BinopExpr BinOp Expr Expr
5254 deriving(Show, Typeable, Data)
5260 deriving(Show, Typeable, Data)
5262 eval :: Expr -> Integer
5263 eval (IntExpr n) = n
5264 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5271 expr = QuasiQuoter parseExprExp parseExprPat
5273 -- Parse an Expr, returning its representation as
5274 -- either a Q Exp or a Q Pat. See the referenced paper
5275 -- for how to use SYB to do this by writing a single
5276 -- parser of type String -> Expr instead of two
5277 -- separate parsers.
5279 parseExprExp :: String -> Q Exp
5282 parseExprPat :: String -> Q Pat
5286 <para>Now run the compiler:
5289 $ ghc --make -XQuasiQuotes Main.hs -o main
5292 <para>Run "main" and here is your output:</para>
5304 <!-- ===================== Arrow notation =================== -->
5306 <sect1 id="arrow-notation">
5307 <title>Arrow notation
5310 <para>Arrows are a generalization of monads introduced by John Hughes.
5311 For more details, see
5316 “Generalising Monads to Arrows”,
5317 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5318 pp67–111, May 2000.
5324 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5325 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5331 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5332 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5338 and the arrows web page at
5339 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5340 With the <option>-XArrows</option> flag, GHC supports the arrow
5341 notation described in the second of these papers.
5342 What follows is a brief introduction to the notation;
5343 it won't make much sense unless you've read Hughes's paper.
5344 This notation is translated to ordinary Haskell,
5345 using combinators from the
5346 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5350 <para>The extension adds a new kind of expression for defining arrows:
5352 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5353 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5355 where <literal>proc</literal> is a new keyword.
5356 The variables of the pattern are bound in the body of the
5357 <literal>proc</literal>-expression,
5358 which is a new sort of thing called a <firstterm>command</firstterm>.
5359 The syntax of commands is as follows:
5361 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5362 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5363 | <replaceable>cmd</replaceable><superscript>0</superscript>
5365 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5366 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5367 infix operators as for expressions, and
5369 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5370 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5371 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5372 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5373 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5374 | <replaceable>fcmd</replaceable>
5376 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5377 | ( <replaceable>cmd</replaceable> )
5378 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5380 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5381 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5382 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5383 | <replaceable>cmd</replaceable>
5385 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5386 except that the bodies are commands instead of expressions.
5390 Commands produce values, but (like monadic computations)
5391 may yield more than one value,
5392 or none, and may do other things as well.
5393 For the most part, familiarity with monadic notation is a good guide to
5395 However the values of expressions, even monadic ones,
5396 are determined by the values of the variables they contain;
5397 this is not necessarily the case for commands.
5401 A simple example of the new notation is the expression
5403 proc x -> f -< x+1
5405 We call this a <firstterm>procedure</firstterm> or
5406 <firstterm>arrow abstraction</firstterm>.
5407 As with a lambda expression, the variable <literal>x</literal>
5408 is a new variable bound within the <literal>proc</literal>-expression.
5409 It refers to the input to the arrow.
5410 In the above example, <literal>-<</literal> is not an identifier but an
5411 new reserved symbol used for building commands from an expression of arrow
5412 type and an expression to be fed as input to that arrow.
5413 (The weird look will make more sense later.)
5414 It may be read as analogue of application for arrows.
5415 The above example is equivalent to the Haskell expression
5417 arr (\ x -> x+1) >>> f
5419 That would make no sense if the expression to the left of
5420 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5421 More generally, the expression to the left of <literal>-<</literal>
5422 may not involve any <firstterm>local variable</firstterm>,
5423 i.e. a variable bound in the current arrow abstraction.
5424 For such a situation there is a variant <literal>-<<</literal>, as in
5426 proc x -> f x -<< x+1
5428 which is equivalent to
5430 arr (\ x -> (f x, x+1)) >>> app
5432 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5434 Such an arrow is equivalent to a monad, so if you're using this form
5435 you may find a monadic formulation more convenient.
5439 <title>do-notation for commands</title>
5442 Another form of command is a form of <literal>do</literal>-notation.
5443 For example, you can write
5452 You can read this much like ordinary <literal>do</literal>-notation,
5453 but with commands in place of monadic expressions.
5454 The first line sends the value of <literal>x+1</literal> as an input to
5455 the arrow <literal>f</literal>, and matches its output against
5456 <literal>y</literal>.
5457 In the next line, the output is discarded.
5458 The arrow <function>returnA</function> is defined in the
5459 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5460 module as <literal>arr id</literal>.
5461 The above example is treated as an abbreviation for
5463 arr (\ x -> (x, x)) >>>
5464 first (arr (\ x -> x+1) >>> f) >>>
5465 arr (\ (y, x) -> (y, (x, y))) >>>
5466 first (arr (\ y -> 2*y) >>> g) >>>
5468 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5469 first (arr (\ (x, z) -> x*z) >>> h) >>>
5470 arr (\ (t, z) -> t+z) >>>
5473 Note that variables not used later in the composition are projected out.
5474 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5476 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5477 module, this reduces to
5479 arr (\ x -> (x+1, x)) >>>
5481 arr (\ (y, x) -> (2*y, (x, y))) >>>
5483 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5485 arr (\ (t, z) -> t+z)
5487 which is what you might have written by hand.
5488 With arrow notation, GHC keeps track of all those tuples of variables for you.
5492 Note that although the above translation suggests that
5493 <literal>let</literal>-bound variables like <literal>z</literal> must be
5494 monomorphic, the actual translation produces Core,
5495 so polymorphic variables are allowed.
5499 It's also possible to have mutually recursive bindings,
5500 using the new <literal>rec</literal> keyword, as in the following example:
5502 counter :: ArrowCircuit a => a Bool Int
5503 counter = proc reset -> do
5504 rec output <- returnA -< if reset then 0 else next
5505 next <- delay 0 -< output+1
5506 returnA -< output
5508 The translation of such forms uses the <function>loop</function> combinator,
5509 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5515 <title>Conditional commands</title>
5518 In the previous example, we used a conditional expression to construct the
5520 Sometimes we want to conditionally execute different commands, as in
5527 which is translated to
5529 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5530 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5532 Since the translation uses <function>|||</function>,
5533 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5537 There are also <literal>case</literal> commands, like
5543 y <- h -< (x1, x2)
5547 The syntax is the same as for <literal>case</literal> expressions,
5548 except that the bodies of the alternatives are commands rather than expressions.
5549 The translation is similar to that of <literal>if</literal> commands.
5555 <title>Defining your own control structures</title>
5558 As we're seen, arrow notation provides constructs,
5559 modelled on those for expressions,
5560 for sequencing, value recursion and conditionals.
5561 But suitable combinators,
5562 which you can define in ordinary Haskell,
5563 may also be used to build new commands out of existing ones.
5564 The basic idea is that a command defines an arrow from environments to values.
5565 These environments assign values to the free local variables of the command.
5566 Thus combinators that produce arrows from arrows
5567 may also be used to build commands from commands.
5568 For example, the <literal>ArrowChoice</literal> class includes a combinator
5570 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5572 so we can use it to build commands:
5574 expr' = proc x -> do
5577 symbol Plus -< ()
5578 y <- term -< ()
5581 symbol Minus -< ()
5582 y <- term -< ()
5585 (The <literal>do</literal> on the first line is needed to prevent the first
5586 <literal><+> ...</literal> from being interpreted as part of the
5587 expression on the previous line.)
5588 This is equivalent to
5590 expr' = (proc x -> returnA -< x)
5591 <+> (proc x -> do
5592 symbol Plus -< ()
5593 y <- term -< ()
5595 <+> (proc x -> do
5596 symbol Minus -< ()
5597 y <- term -< ()
5600 It is essential that this operator be polymorphic in <literal>e</literal>
5601 (representing the environment input to the command
5602 and thence to its subcommands)
5603 and satisfy the corresponding naturality property
5605 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5607 at least for strict <literal>k</literal>.
5608 (This should be automatic if you're not using <function>seq</function>.)
5609 This ensures that environments seen by the subcommands are environments
5610 of the whole command,
5611 and also allows the translation to safely trim these environments.
5612 The operator must also not use any variable defined within the current
5617 We could define our own operator
5619 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5620 untilA body cond = proc x ->
5621 if cond x then returnA -< ()
5624 untilA body cond -< x
5626 and use it in the same way.
5627 Of course this infix syntax only makes sense for binary operators;
5628 there is also a more general syntax involving special brackets:
5632 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5639 <title>Primitive constructs</title>
5642 Some operators will need to pass additional inputs to their subcommands.
5643 For example, in an arrow type supporting exceptions,
5644 the operator that attaches an exception handler will wish to pass the
5645 exception that occurred to the handler.
5646 Such an operator might have a type
5648 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5650 where <literal>Ex</literal> is the type of exceptions handled.
5651 You could then use this with arrow notation by writing a command
5653 body `handleA` \ ex -> handler
5655 so that if an exception is raised in the command <literal>body</literal>,
5656 the variable <literal>ex</literal> is bound to the value of the exception
5657 and the command <literal>handler</literal>,
5658 which typically refers to <literal>ex</literal>, is entered.
5659 Though the syntax here looks like a functional lambda,
5660 we are talking about commands, and something different is going on.
5661 The input to the arrow represented by a command consists of values for
5662 the free local variables in the command, plus a stack of anonymous values.
5663 In all the prior examples, this stack was empty.
5664 In the second argument to <function>handleA</function>,
5665 this stack consists of one value, the value of the exception.
5666 The command form of lambda merely gives this value a name.
5671 the values on the stack are paired to the right of the environment.
5672 So operators like <function>handleA</function> that pass
5673 extra inputs to their subcommands can be designed for use with the notation
5674 by pairing the values with the environment in this way.
5675 More precisely, the type of each argument of the operator (and its result)
5676 should have the form
5678 a (...(e,t1), ... tn) t
5680 where <replaceable>e</replaceable> is a polymorphic variable
5681 (representing the environment)
5682 and <replaceable>ti</replaceable> are the types of the values on the stack,
5683 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5684 The polymorphic variable <replaceable>e</replaceable> must not occur in
5685 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5686 <replaceable>t</replaceable>.
5687 However the arrows involved need not be the same.
5688 Here are some more examples of suitable operators:
5690 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5691 runReader :: ... => a e c -> a' (e,State) c
5692 runState :: ... => a e c -> a' (e,State) (c,State)
5694 We can supply the extra input required by commands built with the last two
5695 by applying them to ordinary expressions, as in
5699 (|runReader (do { ... })|) s
5701 which adds <literal>s</literal> to the stack of inputs to the command
5702 built using <function>runReader</function>.
5706 The command versions of lambda abstraction and application are analogous to
5707 the expression versions.
5708 In particular, the beta and eta rules describe equivalences of commands.
5709 These three features (operators, lambda abstraction and application)
5710 are the core of the notation; everything else can be built using them,
5711 though the results would be somewhat clumsy.
5712 For example, we could simulate <literal>do</literal>-notation by defining
5714 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5715 u `bind` f = returnA &&& u >>> f
5717 bind_ :: Arrow a => a e b -> a e c -> a e c
5718 u `bind_` f = u `bind` (arr fst >>> f)
5720 We could simulate <literal>if</literal> by defining
5722 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5723 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5730 <title>Differences with the paper</title>
5735 <para>Instead of a single form of arrow application (arrow tail) with two
5736 translations, the implementation provides two forms
5737 <quote><literal>-<</literal></quote> (first-order)
5738 and <quote><literal>-<<</literal></quote> (higher-order).
5743 <para>User-defined operators are flagged with banana brackets instead of
5744 a new <literal>form</literal> keyword.
5753 <title>Portability</title>
5756 Although only GHC implements arrow notation directly,
5757 there is also a preprocessor
5759 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5760 that translates arrow notation into Haskell 98
5761 for use with other Haskell systems.
5762 You would still want to check arrow programs with GHC;
5763 tracing type errors in the preprocessor output is not easy.
5764 Modules intended for both GHC and the preprocessor must observe some
5765 additional restrictions:
5770 The module must import
5771 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5777 The preprocessor cannot cope with other Haskell extensions.
5778 These would have to go in separate modules.
5784 Because the preprocessor targets Haskell (rather than Core),
5785 <literal>let</literal>-bound variables are monomorphic.
5796 <!-- ==================== BANG PATTERNS ================= -->
5798 <sect1 id="bang-patterns">
5799 <title>Bang patterns
5800 <indexterm><primary>Bang patterns</primary></indexterm>
5802 <para>GHC supports an extension of pattern matching called <emphasis>bang
5803 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5805 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5806 prime feature description</ulink> contains more discussion and examples
5807 than the material below.
5810 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5813 <sect2 id="bang-patterns-informal">
5814 <title>Informal description of bang patterns
5817 The main idea is to add a single new production to the syntax of patterns:
5821 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5822 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5827 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5828 whereas without the bang it would be lazy.
5829 Bang patterns can be nested of course:
5833 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5834 <literal>y</literal>.
5835 A bang only really has an effect if it precedes a variable or wild-card pattern:
5840 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5841 forces evaluation anyway does nothing.
5843 Bang patterns work in <literal>case</literal> expressions too, of course:
5845 g5 x = let y = f x in body
5846 g6 x = case f x of { y -> body }
5847 g7 x = case f x of { !y -> body }
5849 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5850 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5851 result, and then evaluates <literal>body</literal>.
5853 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5854 definitions too. For example:
5858 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5859 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5860 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5861 in a function argument <literal>![x,y]</literal> means the
5862 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5863 is part of the syntax of <literal>let</literal> bindings.
5868 <sect2 id="bang-patterns-sem">
5869 <title>Syntax and semantics
5873 We add a single new production to the syntax of patterns:
5877 There is one problem with syntactic ambiguity. Consider:
5881 Is this a definition of the infix function "<literal>(!)</literal>",
5882 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5883 ambiguity in favour of the latter. If you want to define
5884 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5889 The semantics of Haskell pattern matching is described in <ulink
5890 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5891 Section 3.17.2</ulink> of the Haskell Report. To this description add
5892 one extra item 10, saying:
5893 <itemizedlist><listitem><para>Matching
5894 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5895 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5896 <listitem><para>otherwise, <literal>pat</literal> is matched against
5897 <literal>v</literal></para></listitem>
5899 </para></listitem></itemizedlist>
5900 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5901 Section 3.17.3</ulink>, add a new case (t):
5903 case v of { !pat -> e; _ -> e' }
5904 = v `seq` case v of { pat -> e; _ -> e' }
5907 That leaves let expressions, whose translation is given in
5908 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
5910 of the Haskell Report.
5911 In the translation box, first apply
5912 the following transformation: for each pattern <literal>pi</literal> that is of
5913 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5914 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5915 have a bang at the top, apply the rules in the existing box.
5917 <para>The effect of the let rule is to force complete matching of the pattern
5918 <literal>qi</literal> before evaluation of the body is begun. The bang is
5919 retained in the translated form in case <literal>qi</literal> is a variable,
5927 The let-binding can be recursive. However, it is much more common for
5928 the let-binding to be non-recursive, in which case the following law holds:
5929 <literal>(let !p = rhs in body)</literal>
5931 <literal>(case rhs of !p -> body)</literal>
5934 A pattern with a bang at the outermost level is not allowed at the top level of
5940 <!-- ==================== ASSERTIONS ================= -->
5942 <sect1 id="assertions">
5944 <indexterm><primary>Assertions</primary></indexterm>
5948 If you want to make use of assertions in your standard Haskell code, you
5949 could define a function like the following:
5955 assert :: Bool -> a -> a
5956 assert False x = error "assertion failed!"
5963 which works, but gives you back a less than useful error message --
5964 an assertion failed, but which and where?
5968 One way out is to define an extended <function>assert</function> function which also
5969 takes a descriptive string to include in the error message and
5970 perhaps combine this with the use of a pre-processor which inserts
5971 the source location where <function>assert</function> was used.
5975 Ghc offers a helping hand here, doing all of this for you. For every
5976 use of <function>assert</function> in the user's source:
5982 kelvinToC :: Double -> Double
5983 kelvinToC k = assert (k >= 0.0) (k+273.15)
5989 Ghc will rewrite this to also include the source location where the
5996 assert pred val ==> assertError "Main.hs|15" pred val
6002 The rewrite is only performed by the compiler when it spots
6003 applications of <function>Control.Exception.assert</function>, so you
6004 can still define and use your own versions of
6005 <function>assert</function>, should you so wish. If not, import
6006 <literal>Control.Exception</literal> to make use
6007 <function>assert</function> in your code.
6011 GHC ignores assertions when optimisation is turned on with the
6012 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6013 <literal>assert pred e</literal> will be rewritten to
6014 <literal>e</literal>. You can also disable assertions using the
6015 <option>-fignore-asserts</option>
6016 option<indexterm><primary><option>-fignore-asserts</option></primary>
6017 </indexterm>.</para>
6020 Assertion failures can be caught, see the documentation for the
6021 <literal>Control.Exception</literal> library for the details.
6027 <!-- =============================== PRAGMAS =========================== -->
6029 <sect1 id="pragmas">
6030 <title>Pragmas</title>
6032 <indexterm><primary>pragma</primary></indexterm>
6034 <para>GHC supports several pragmas, or instructions to the
6035 compiler placed in the source code. Pragmas don't normally affect
6036 the meaning of the program, but they might affect the efficiency
6037 of the generated code.</para>
6039 <para>Pragmas all take the form
6041 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6043 where <replaceable>word</replaceable> indicates the type of
6044 pragma, and is followed optionally by information specific to that
6045 type of pragma. Case is ignored in
6046 <replaceable>word</replaceable>. The various values for
6047 <replaceable>word</replaceable> that GHC understands are described
6048 in the following sections; any pragma encountered with an
6049 unrecognised <replaceable>word</replaceable> is (silently)
6050 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6051 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6053 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6054 pragma must precede the <literal>module</literal> keyword in the file.
6055 There can be as many file-header pragmas as you please, and they can be
6056 preceded or followed by comments.</para>
6058 <sect2 id="language-pragma">
6059 <title>LANGUAGE pragma</title>
6061 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6062 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6064 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6066 It is the intention that all Haskell compilers support the
6067 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6068 all extensions are supported by all compilers, of
6069 course. The <literal>LANGUAGE</literal> pragma should be used instead
6070 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6072 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6074 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6076 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6078 <para>Every language extension can also be turned into a command-line flag
6079 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6080 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6083 <para>A list of all supported language extensions can be obtained by invoking
6084 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6086 <para>Any extension from the <literal>Extension</literal> type defined in
6088 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6089 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6093 <sect2 id="options-pragma">
6094 <title>OPTIONS_GHC pragma</title>
6095 <indexterm><primary>OPTIONS_GHC</primary>
6097 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6100 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6101 additional options that are given to the compiler when compiling
6102 this source file. See <xref linkend="source-file-options"/> for
6105 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6106 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6109 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6111 <sect2 id="include-pragma">
6112 <title>INCLUDE pragma</title>
6114 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6115 of C header files that should be <literal>#include</literal>'d into
6116 the C source code generated by the compiler for the current module (if
6117 compiling via C). For example:</para>
6120 {-# INCLUDE "foo.h" #-}
6121 {-# INCLUDE <stdio.h> #-}</programlisting>
6123 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6125 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6126 to the <option>-#include</option> option (<xref
6127 linkend="options-C-compiler" />), because the
6128 <literal>INCLUDE</literal> pragma is understood by other
6129 compilers. Yet another alternative is to add the include file to each
6130 <literal>foreign import</literal> declaration in your code, but we
6131 don't recommend using this approach with GHC.</para>
6134 <sect2 id="warning-deprecated-pragma">
6135 <title>WARNING and DEPRECATED pragmas</title>
6136 <indexterm><primary>WARNING</primary></indexterm>
6137 <indexterm><primary>DEPRECATED</primary></indexterm>
6139 <para>The WARNING pragma allows you to attach an arbitrary warning
6140 to a particular function, class, or type.
6141 A DEPRECATED pragma lets you specify that
6142 a particular function, class, or type is deprecated.
6143 There are two ways of using these pragmas.
6147 <para>You can work on an entire module thus:</para>
6149 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6154 module Wibble {-# WARNING "This is an unstable interface." #-} where
6157 <para>When you compile any module that import
6158 <literal>Wibble</literal>, GHC will print the specified
6163 <para>You can attach a warning to a function, class, type, or data constructor, with the
6164 following top-level declarations:</para>
6166 {-# DEPRECATED f, C, T "Don't use these" #-}
6167 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6169 <para>When you compile any module that imports and uses any
6170 of the specified entities, GHC will print the specified
6172 <para> You can only attach to entities declared at top level in the module
6173 being compiled, and you can only use unqualified names in the list of
6174 entities. A capitalised name, such as <literal>T</literal>
6175 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6176 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6177 both are in scope. If both are in scope, there is currently no way to
6178 specify one without the other (c.f. fixities
6179 <xref linkend="infix-tycons"/>).</para>
6182 Warnings and deprecations are not reported for
6183 (a) uses within the defining module, and
6184 (b) uses in an export list.
6185 The latter reduces spurious complaints within a library
6186 in which one module gathers together and re-exports
6187 the exports of several others.
6189 <para>You can suppress the warnings with the flag
6190 <option>-fno-warn-warnings-deprecations</option>.</para>
6193 <sect2 id="inline-noinline-pragma">
6194 <title>INLINE and NOINLINE pragmas</title>
6196 <para>These pragmas control the inlining of function
6199 <sect3 id="inline-pragma">
6200 <title>INLINE pragma</title>
6201 <indexterm><primary>INLINE</primary></indexterm>
6203 <para>GHC (with <option>-O</option>, as always) tries to
6204 inline (or “unfold”) functions/values that are
6205 “small enough,” thus avoiding the call overhead
6206 and possibly exposing other more-wonderful optimisations.
6207 Normally, if GHC decides a function is “too
6208 expensive” to inline, it will not do so, nor will it
6209 export that unfolding for other modules to use.</para>
6211 <para>The sledgehammer you can bring to bear is the
6212 <literal>INLINE</literal><indexterm><primary>INLINE
6213 pragma</primary></indexterm> pragma, used thusly:</para>
6216 key_function :: Int -> String -> (Bool, Double)
6217 {-# INLINE key_function #-}
6220 <para>The major effect of an <literal>INLINE</literal> pragma
6221 is to declare a function's “cost” to be very low.
6222 The normal unfolding machinery will then be very keen to
6223 inline it. However, an <literal>INLINE</literal> pragma for a
6224 function "<literal>f</literal>" has a number of other effects:
6227 No functions are inlined into <literal>f</literal>. Otherwise
6228 GHC might inline a big function into <literal>f</literal>'s right hand side,
6229 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6232 The float-in, float-out, and common-sub-expression transformations are not
6233 applied to the body of <literal>f</literal>.
6236 An INLINE function is not worker/wrappered by strictness analysis.
6237 It's going to be inlined wholesale instead.
6240 All of these effects are aimed at ensuring that what gets inlined is
6241 exactly what you asked for, no more and no less.
6243 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6244 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6245 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6246 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6247 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6248 when there is no choice even an INLINE function can be selected, in which case
6249 the INLINE pragma is ignored.
6250 For example, for a self-recursive function, the loop breaker can only be the function
6251 itself, so an INLINE pragma is always ignored.</para>
6253 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6254 function can be put anywhere its type signature could be
6257 <para><literal>INLINE</literal> pragmas are a particularly
6259 <literal>then</literal>/<literal>return</literal> (or
6260 <literal>bind</literal>/<literal>unit</literal>) functions in
6261 a monad. For example, in GHC's own
6262 <literal>UniqueSupply</literal> monad code, we have:</para>
6265 {-# INLINE thenUs #-}
6266 {-# INLINE returnUs #-}
6269 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6270 linkend="noinline-pragma"/>).</para>
6272 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
6273 so if you want your code to be HBC-compatible you'll have to surround
6274 the pragma with C pre-processor directives
6275 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
6279 <sect3 id="noinline-pragma">
6280 <title>NOINLINE pragma</title>
6282 <indexterm><primary>NOINLINE</primary></indexterm>
6283 <indexterm><primary>NOTINLINE</primary></indexterm>
6285 <para>The <literal>NOINLINE</literal> pragma does exactly what
6286 you'd expect: it stops the named function from being inlined
6287 by the compiler. You shouldn't ever need to do this, unless
6288 you're very cautious about code size.</para>
6290 <para><literal>NOTINLINE</literal> is a synonym for
6291 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6292 specified by Haskell 98 as the standard way to disable
6293 inlining, so it should be used if you want your code to be
6297 <sect3 id="phase-control">
6298 <title>Phase control</title>
6300 <para> Sometimes you want to control exactly when in GHC's
6301 pipeline the INLINE pragma is switched on. Inlining happens
6302 only during runs of the <emphasis>simplifier</emphasis>. Each
6303 run of the simplifier has a different <emphasis>phase
6304 number</emphasis>; the phase number decreases towards zero.
6305 If you use <option>-dverbose-core2core</option> you'll see the
6306 sequence of phase numbers for successive runs of the
6307 simplifier. In an INLINE pragma you can optionally specify a
6311 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6312 <literal>f</literal>
6313 until phase <literal>k</literal>, but from phase
6314 <literal>k</literal> onwards be very keen to inline it.
6317 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6318 <literal>f</literal>
6319 until phase <literal>k</literal>, but from phase
6320 <literal>k</literal> onwards do not inline it.
6323 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6324 <literal>f</literal>
6325 until phase <literal>k</literal>, but from phase
6326 <literal>k</literal> onwards be willing to inline it (as if
6327 there was no pragma).
6330 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6331 <literal>f</literal>
6332 until phase <literal>k</literal>, but from phase
6333 <literal>k</literal> onwards do not inline it.
6336 The same information is summarised here:
6338 -- Before phase 2 Phase 2 and later
6339 {-# INLINE [2] f #-} -- No Yes
6340 {-# INLINE [~2] f #-} -- Yes No
6341 {-# NOINLINE [2] f #-} -- No Maybe
6342 {-# NOINLINE [~2] f #-} -- Maybe No
6344 {-# INLINE f #-} -- Yes Yes
6345 {-# NOINLINE f #-} -- No No
6347 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6348 function body is small, or it is applied to interesting-looking arguments etc).
6349 Another way to understand the semantics is this:
6351 <listitem><para>For both INLINE and NOINLINE, the phase number says
6352 when inlining is allowed at all.</para></listitem>
6353 <listitem><para>The INLINE pragma has the additional effect of making the
6354 function body look small, so that when inlining is allowed it is very likely to
6359 <para>The same phase-numbering control is available for RULES
6360 (<xref linkend="rewrite-rules"/>).</para>
6364 <sect2 id="line-pragma">
6365 <title>LINE pragma</title>
6367 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6368 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6369 <para>This pragma is similar to C's <literal>#line</literal>
6370 pragma, and is mainly for use in automatically generated Haskell
6371 code. It lets you specify the line number and filename of the
6372 original code; for example</para>
6374 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6376 <para>if you'd generated the current file from something called
6377 <filename>Foo.vhs</filename> and this line corresponds to line
6378 42 in the original. GHC will adjust its error messages to refer
6379 to the line/file named in the <literal>LINE</literal>
6384 <title>RULES pragma</title>
6386 <para>The RULES pragma lets you specify rewrite rules. It is
6387 described in <xref linkend="rewrite-rules"/>.</para>
6390 <sect2 id="specialize-pragma">
6391 <title>SPECIALIZE pragma</title>
6393 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6394 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6395 <indexterm><primary>overloading, death to</primary></indexterm>
6397 <para>(UK spelling also accepted.) For key overloaded
6398 functions, you can create extra versions (NB: more code space)
6399 specialised to particular types. Thus, if you have an
6400 overloaded function:</para>
6403 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6406 <para>If it is heavily used on lists with
6407 <literal>Widget</literal> keys, you could specialise it as
6411 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6414 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6415 be put anywhere its type signature could be put.</para>
6417 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6418 (a) a specialised version of the function and (b) a rewrite rule
6419 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6420 un-specialised function into a call to the specialised one.</para>
6422 <para>The type in a SPECIALIZE pragma can be any type that is less
6423 polymorphic than the type of the original function. In concrete terms,
6424 if the original function is <literal>f</literal> then the pragma
6426 {-# SPECIALIZE f :: <type> #-}
6428 is valid if and only if the definition
6430 f_spec :: <type>
6433 is valid. Here are some examples (where we only give the type signature
6434 for the original function, not its code):
6436 f :: Eq a => a -> b -> b
6437 {-# SPECIALISE f :: Int -> b -> b #-}
6439 g :: (Eq a, Ix b) => a -> b -> b
6440 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6442 h :: Eq a => a -> a -> a
6443 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6445 The last of these examples will generate a
6446 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6447 well. If you use this kind of specialisation, let us know how well it works.
6450 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6451 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6452 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6453 The <literal>INLINE</literal> pragma affects the specialised version of the
6454 function (only), and applies even if the function is recursive. The motivating
6457 -- A GADT for arrays with type-indexed representation
6459 ArrInt :: !Int -> ByteArray# -> Arr Int
6460 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6462 (!:) :: Arr e -> Int -> e
6463 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6464 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6465 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6466 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6468 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6469 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6470 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6471 the specialised function will be inlined. It has two calls to
6472 <literal>(!:)</literal>,
6473 both at type <literal>Int</literal>. Both these calls fire the first
6474 specialisation, whose body is also inlined. The result is a type-based
6475 unrolling of the indexing function.</para>
6476 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6477 on an ordinarily-recursive function.</para>
6479 <para>Note: In earlier versions of GHC, it was possible to provide your own
6480 specialised function for a given type:
6483 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6486 This feature has been removed, as it is now subsumed by the
6487 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6491 <sect2 id="specialize-instance-pragma">
6492 <title>SPECIALIZE instance pragma
6496 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6497 <indexterm><primary>overloading, death to</primary></indexterm>
6498 Same idea, except for instance declarations. For example:
6501 instance (Eq a) => Eq (Foo a) where {
6502 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6506 The pragma must occur inside the <literal>where</literal> part
6507 of the instance declaration.
6510 Compatible with HBC, by the way, except perhaps in the placement
6516 <sect2 id="unpack-pragma">
6517 <title>UNPACK pragma</title>
6519 <indexterm><primary>UNPACK</primary></indexterm>
6521 <para>The <literal>UNPACK</literal> indicates to the compiler
6522 that it should unpack the contents of a constructor field into
6523 the constructor itself, removing a level of indirection. For
6527 data T = T {-# UNPACK #-} !Float
6528 {-# UNPACK #-} !Float
6531 <para>will create a constructor <literal>T</literal> containing
6532 two unboxed floats. This may not always be an optimisation: if
6533 the <function>T</function> constructor is scrutinised and the
6534 floats passed to a non-strict function for example, they will
6535 have to be reboxed (this is done automatically by the
6538 <para>Unpacking constructor fields should only be used in
6539 conjunction with <option>-O</option>, in order to expose
6540 unfoldings to the compiler so the reboxing can be removed as
6541 often as possible. For example:</para>
6545 f (T f1 f2) = f1 + f2
6548 <para>The compiler will avoid reboxing <function>f1</function>
6549 and <function>f2</function> by inlining <function>+</function>
6550 on floats, but only when <option>-O</option> is on.</para>
6552 <para>Any single-constructor data is eligible for unpacking; for
6556 data T = T {-# UNPACK #-} !(Int,Int)
6559 <para>will store the two <literal>Int</literal>s directly in the
6560 <function>T</function> constructor, by flattening the pair.
6561 Multi-level unpacking is also supported:
6564 data T = T {-# UNPACK #-} !S
6565 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6568 will store two unboxed <literal>Int#</literal>s
6569 directly in the <function>T</function> constructor. The
6570 unpacker can see through newtypes, too.</para>
6572 <para>If a field cannot be unpacked, you will not get a warning,
6573 so it might be an idea to check the generated code with
6574 <option>-ddump-simpl</option>.</para>
6576 <para>See also the <option>-funbox-strict-fields</option> flag,
6577 which essentially has the effect of adding
6578 <literal>{-# UNPACK #-}</literal> to every strict
6579 constructor field.</para>
6582 <sect2 id="source-pragma">
6583 <title>SOURCE pragma</title>
6585 <indexterm><primary>SOURCE</primary></indexterm>
6586 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6587 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6593 <!-- ======================= REWRITE RULES ======================== -->
6595 <sect1 id="rewrite-rules">
6596 <title>Rewrite rules
6598 <indexterm><primary>RULES pragma</primary></indexterm>
6599 <indexterm><primary>pragma, RULES</primary></indexterm>
6600 <indexterm><primary>rewrite rules</primary></indexterm></title>
6603 The programmer can specify rewrite rules as part of the source program
6609 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6614 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
6615 If you need more information, then <option>-ddump-rule-firings</option> shows you
6616 each individual rule firing in detail.
6620 <title>Syntax</title>
6623 From a syntactic point of view:
6629 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6630 may be generated by the layout rule).
6636 The layout rule applies in a pragma.
6637 Currently no new indentation level
6638 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6639 you must lay out the starting in the same column as the enclosing definitions.
6642 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6643 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6646 Furthermore, the closing <literal>#-}</literal>
6647 should start in a column to the right of the opening <literal>{-#</literal>.
6653 Each rule has a name, enclosed in double quotes. The name itself has
6654 no significance at all. It is only used when reporting how many times the rule fired.
6660 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6661 immediately after the name of the rule. Thus:
6664 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6667 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6668 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6677 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6678 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6679 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6680 by spaces, just like in a type <literal>forall</literal>.
6686 A pattern variable may optionally have a type signature.
6687 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6688 For example, here is the <literal>foldr/build</literal> rule:
6691 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6692 foldr k z (build g) = g k z
6695 Since <function>g</function> has a polymorphic type, it must have a type signature.
6702 The left hand side of a rule must consist of a top-level variable applied
6703 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6706 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6707 "wrong2" forall f. f True = True
6710 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6717 A rule does not need to be in the same module as (any of) the
6718 variables it mentions, though of course they need to be in scope.
6724 All rules are implicitly exported from the module, and are therefore
6725 in force in any module that imports the module that defined the rule, directly
6726 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6727 in force when compiling A.) The situation is very similar to that for instance
6735 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
6736 any other flag settings. Furthermore, inside a RULE, the language extension
6737 <option>-XScopedTypeVariables</option> is automatically enabled; see
6738 <xref linkend="scoped-type-variables"/>.
6744 Like other pragmas, RULE pragmas are always checked for scope errors, and
6745 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
6746 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
6747 if the <option>-fenable-rewrite-rules</option> flag is
6748 on (see <xref linkend="rule-semantics"/>).
6757 <sect2 id="rule-semantics">
6758 <title>Semantics</title>
6761 From a semantic point of view:
6766 Rules are enabled (that is, used during optimisation)
6767 by the <option>-fenable-rewrite-rules</option> flag.
6768 This flag is implied by <option>-O</option>, and may be switched
6769 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
6770 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
6771 may not do what you expect, though, because without <option>-O</option> GHC
6772 ignores all optimisation information in interface files;
6773 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
6774 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
6775 has no effect on parsing or typechecking.
6781 Rules are regarded as left-to-right rewrite rules.
6782 When GHC finds an expression that is a substitution instance of the LHS
6783 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6784 By "a substitution instance" we mean that the LHS can be made equal to the
6785 expression by substituting for the pattern variables.
6792 GHC makes absolutely no attempt to verify that the LHS and RHS
6793 of a rule have the same meaning. That is undecidable in general, and
6794 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6801 GHC makes no attempt to make sure that the rules are confluent or
6802 terminating. For example:
6805 "loop" forall x y. f x y = f y x
6808 This rule will cause the compiler to go into an infinite loop.
6815 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6821 GHC currently uses a very simple, syntactic, matching algorithm
6822 for matching a rule LHS with an expression. It seeks a substitution
6823 which makes the LHS and expression syntactically equal modulo alpha
6824 conversion. The pattern (rule), but not the expression, is eta-expanded if
6825 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6826 But not beta conversion (that's called higher-order matching).
6830 Matching is carried out on GHC's intermediate language, which includes
6831 type abstractions and applications. So a rule only matches if the
6832 types match too. See <xref linkend="rule-spec"/> below.
6838 GHC keeps trying to apply the rules as it optimises the program.
6839 For example, consider:
6848 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6849 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6850 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6851 not be substituted, and the rule would not fire.
6858 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
6859 results. Consider this (artificial) example
6862 {-# RULES "f" f True = False #-}
6868 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
6873 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
6875 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
6876 would have been a better chance that <literal>f</literal>'s RULE might fire.
6879 The way to get predictable behaviour is to use a NOINLINE
6880 pragma on <literal>f</literal>, to ensure
6881 that it is not inlined until its RULEs have had a chance to fire.
6891 <title>List fusion</title>
6894 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6895 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6896 intermediate list should be eliminated entirely.
6900 The following are good producers:
6912 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6918 Explicit lists (e.g. <literal>[True, False]</literal>)
6924 The cons constructor (e.g <literal>3:4:[]</literal>)
6930 <function>++</function>
6936 <function>map</function>
6942 <function>take</function>, <function>filter</function>
6948 <function>iterate</function>, <function>repeat</function>
6954 <function>zip</function>, <function>zipWith</function>
6963 The following are good consumers:
6975 <function>array</function> (on its second argument)
6981 <function>++</function> (on its first argument)
6987 <function>foldr</function>
6993 <function>map</function>
6999 <function>take</function>, <function>filter</function>
7005 <function>concat</function>
7011 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7017 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7018 will fuse with one but not the other)
7024 <function>partition</function>
7030 <function>head</function>
7036 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7042 <function>sequence_</function>
7048 <function>msum</function>
7054 <function>sortBy</function>
7063 So, for example, the following should generate no intermediate lists:
7066 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7072 This list could readily be extended; if there are Prelude functions that you use
7073 a lot which are not included, please tell us.
7077 If you want to write your own good consumers or producers, look at the
7078 Prelude definitions of the above functions to see how to do so.
7083 <sect2 id="rule-spec">
7084 <title>Specialisation
7088 Rewrite rules can be used to get the same effect as a feature
7089 present in earlier versions of GHC.
7090 For example, suppose that:
7093 genericLookup :: Ord a => Table a b -> a -> b
7094 intLookup :: Table Int b -> Int -> b
7097 where <function>intLookup</function> is an implementation of
7098 <function>genericLookup</function> that works very fast for
7099 keys of type <literal>Int</literal>. You might wish
7100 to tell GHC to use <function>intLookup</function> instead of
7101 <function>genericLookup</function> whenever the latter was called with
7102 type <literal>Table Int b -> Int -> b</literal>.
7103 It used to be possible to write
7106 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7109 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7112 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7115 This slightly odd-looking rule instructs GHC to replace
7116 <function>genericLookup</function> by <function>intLookup</function>
7117 <emphasis>whenever the types match</emphasis>.
7118 What is more, this rule does not need to be in the same
7119 file as <function>genericLookup</function>, unlike the
7120 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7121 have an original definition available to specialise).
7124 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7125 <function>intLookup</function> really behaves as a specialised version
7126 of <function>genericLookup</function>!!!</para>
7128 <para>An example in which using <literal>RULES</literal> for
7129 specialisation will Win Big:
7132 toDouble :: Real a => a -> Double
7133 toDouble = fromRational . toRational
7135 {-# RULES "toDouble/Int" toDouble = i2d #-}
7136 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7139 The <function>i2d</function> function is virtually one machine
7140 instruction; the default conversion—via an intermediate
7141 <literal>Rational</literal>—is obscenely expensive by
7148 <title>Controlling what's going on</title>
7156 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7162 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7163 If you add <option>-dppr-debug</option> you get a more detailed listing.
7169 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7172 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7173 {-# INLINE build #-}
7177 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7178 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7179 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7180 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7187 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7188 see how to write rules that will do fusion and yet give an efficient
7189 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7199 <sect2 id="core-pragma">
7200 <title>CORE pragma</title>
7202 <indexterm><primary>CORE pragma</primary></indexterm>
7203 <indexterm><primary>pragma, CORE</primary></indexterm>
7204 <indexterm><primary>core, annotation</primary></indexterm>
7207 The external core format supports <quote>Note</quote> annotations;
7208 the <literal>CORE</literal> pragma gives a way to specify what these
7209 should be in your Haskell source code. Syntactically, core
7210 annotations are attached to expressions and take a Haskell string
7211 literal as an argument. The following function definition shows an
7215 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7218 Semantically, this is equivalent to:
7226 However, when external core is generated (via
7227 <option>-fext-core</option>), there will be Notes attached to the
7228 expressions <function>show</function> and <varname>x</varname>.
7229 The core function declaration for <function>f</function> is:
7233 f :: %forall a . GHCziShow.ZCTShow a ->
7234 a -> GHCziBase.ZMZN GHCziBase.Char =
7235 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7237 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7239 (tpl1::GHCziBase.Int ->
7241 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7243 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7244 (tpl3::GHCziBase.ZMZN a ->
7245 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7253 Here, we can see that the function <function>show</function> (which
7254 has been expanded out to a case expression over the Show dictionary)
7255 has a <literal>%note</literal> attached to it, as does the
7256 expression <varname>eta</varname> (which used to be called
7257 <varname>x</varname>).
7264 <sect1 id="special-ids">
7265 <title>Special built-in functions</title>
7266 <para>GHC has a few built-in functions with special behaviour. These
7267 are now described in the module <ulink
7268 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7269 in the library documentation.</para>
7273 <sect1 id="generic-classes">
7274 <title>Generic classes</title>
7277 The ideas behind this extension are described in detail in "Derivable type classes",
7278 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7279 An example will give the idea:
7287 fromBin :: [Int] -> (a, [Int])
7289 toBin {| Unit |} Unit = []
7290 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7291 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7292 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7294 fromBin {| Unit |} bs = (Unit, bs)
7295 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7296 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7297 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7298 (y,bs'') = fromBin bs'
7301 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7302 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7303 which are defined thus in the library module <literal>Generics</literal>:
7307 data a :+: b = Inl a | Inr b
7308 data a :*: b = a :*: b
7311 Now you can make a data type into an instance of Bin like this:
7313 instance (Bin a, Bin b) => Bin (a,b)
7314 instance Bin a => Bin [a]
7316 That is, just leave off the "where" clause. Of course, you can put in the
7317 where clause and over-ride whichever methods you please.
7321 <title> Using generics </title>
7322 <para>To use generics you need to</para>
7325 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7326 <option>-XGenerics</option> (to generate extra per-data-type code),
7327 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7331 <para>Import the module <literal>Generics</literal> from the
7332 <literal>lang</literal> package. This import brings into
7333 scope the data types <literal>Unit</literal>,
7334 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7335 don't need this import if you don't mention these types
7336 explicitly; for example, if you are simply giving instance
7337 declarations.)</para>
7342 <sect2> <title> Changes wrt the paper </title>
7344 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7345 can be written infix (indeed, you can now use
7346 any operator starting in a colon as an infix type constructor). Also note that
7347 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7348 Finally, note that the syntax of the type patterns in the class declaration
7349 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7350 alone would ambiguous when they appear on right hand sides (an extension we
7351 anticipate wanting).
7355 <sect2> <title>Terminology and restrictions</title>
7357 Terminology. A "generic default method" in a class declaration
7358 is one that is defined using type patterns as above.
7359 A "polymorphic default method" is a default method defined as in Haskell 98.
7360 A "generic class declaration" is a class declaration with at least one
7361 generic default method.
7369 Alas, we do not yet implement the stuff about constructor names and
7376 A generic class can have only one parameter; you can't have a generic
7377 multi-parameter class.
7383 A default method must be defined entirely using type patterns, or entirely
7384 without. So this is illegal:
7387 op :: a -> (a, Bool)
7388 op {| Unit |} Unit = (Unit, True)
7391 However it is perfectly OK for some methods of a generic class to have
7392 generic default methods and others to have polymorphic default methods.
7398 The type variable(s) in the type pattern for a generic method declaration
7399 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:
7403 op {| p :*: q |} (x :*: y) = op (x :: p)
7411 The type patterns in a generic default method must take one of the forms:
7417 where "a" and "b" are type variables. Furthermore, all the type patterns for
7418 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7419 must use the same type variables. So this is illegal:
7423 op {| a :+: b |} (Inl x) = True
7424 op {| p :+: q |} (Inr y) = False
7426 The type patterns must be identical, even in equations for different methods of the class.
7427 So this too is illegal:
7431 op1 {| a :*: b |} (x :*: y) = True
7434 op2 {| p :*: q |} (x :*: y) = False
7436 (The reason for this restriction is that we gather all the equations for a particular type constructor
7437 into a single generic instance declaration.)
7443 A generic method declaration must give a case for each of the three type constructors.
7449 The type for a generic method can be built only from:
7451 <listitem> <para> Function arrows </para> </listitem>
7452 <listitem> <para> Type variables </para> </listitem>
7453 <listitem> <para> Tuples </para> </listitem>
7454 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7456 Here are some example type signatures for generic methods:
7459 op2 :: Bool -> (a,Bool)
7460 op3 :: [Int] -> a -> a
7463 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7467 This restriction is an implementation restriction: we just haven't got around to
7468 implementing the necessary bidirectional maps over arbitrary type constructors.
7469 It would be relatively easy to add specific type constructors, such as Maybe and list,
7470 to the ones that are allowed.</para>
7475 In an instance declaration for a generic class, the idea is that the compiler
7476 will fill in the methods for you, based on the generic templates. However it can only
7481 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7486 No constructor of the instance type has unboxed fields.
7490 (Of course, these things can only arise if you are already using GHC extensions.)
7491 However, you can still give an instance declarations for types which break these rules,
7492 provided you give explicit code to override any generic default methods.
7500 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7501 what the compiler does with generic declarations.
7506 <sect2> <title> Another example </title>
7508 Just to finish with, here's another example I rather like:
7512 nCons {| Unit |} _ = 1
7513 nCons {| a :*: b |} _ = 1
7514 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7517 tag {| Unit |} _ = 1
7518 tag {| a :*: b |} _ = 1
7519 tag {| a :+: b |} (Inl x) = tag x
7520 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7526 <sect1 id="monomorphism">
7527 <title>Control over monomorphism</title>
7529 <para>GHC supports two flags that control the way in which generalisation is
7530 carried out at let and where bindings.
7534 <title>Switching off the dreaded Monomorphism Restriction</title>
7535 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7537 <para>Haskell's monomorphism restriction (see
7538 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7540 of the Haskell Report)
7541 can be completely switched off by
7542 <option>-XNoMonomorphismRestriction</option>.
7547 <title>Monomorphic pattern bindings</title>
7548 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7549 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7551 <para> As an experimental change, we are exploring the possibility of
7552 making pattern bindings monomorphic; that is, not generalised at all.
7553 A pattern binding is a binding whose LHS has no function arguments,
7554 and is not a simple variable. For example:
7556 f x = x -- Not a pattern binding
7557 f = \x -> x -- Not a pattern binding
7558 f :: Int -> Int = \x -> x -- Not a pattern binding
7560 (g,h) = e -- A pattern binding
7561 (f) = e -- A pattern binding
7562 [x] = e -- A pattern binding
7564 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7565 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7574 ;;; Local Variables: ***
7576 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7577 ;;; ispell-local-dictionary: "british" ***
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