2 <IndexTerm><Primary>language, GHC</Primary></IndexTerm>
3 <IndexTerm><Primary>extensions, GHC</Primary></IndexTerm>
4 As with all known Haskell systems, GHC implements some extensions to
5 the language. To use them, you'll need to give a <Option>-fglasgow-exts</Option>
6 <IndexTerm><Primary>-fglasgow-exts option</Primary></IndexTerm> option.
10 Virtually all of the Glasgow extensions serve to give you access to
11 the underlying facilities with which we implement Haskell. Thus, you
12 can get at the Raw Iron, if you are willing to write some non-standard
13 code at a more primitive level. You need not be “stuck” on
14 performance because of the implementation costs of Haskell's
15 “high-level” features—you can always code “under” them. In an extreme case, you can write all your time-critical code in C, and then just glue it together with Haskell!
19 Executive summary of our extensions:
26 <Term>Unboxed types and primitive operations:</Term>
29 You can get right down to the raw machine types and operations;
30 included in this are “primitive arrays” (direct access to Big Wads
31 of Bytes). Please see <XRef LinkEnd="glasgow-unboxed"> and following.
37 <Term>Multi-parameter type classes:</Term>
40 GHC's type system supports extended type classes with multiple
41 parameters. Please see <XRef LinkEnd="multi-param-type-classes">.
47 <Term>Local universal quantification:</Term>
50 GHC's type system supports explicit universal quantification in
51 constructor fields and function arguments. This is useful for things
52 like defining <Literal>runST</Literal> from the state-thread world. See <XRef LinkEnd="universal-quantification">.
58 <Term>Extistentially quantification in data types:</Term>
61 Some or all of the type variables in a datatype declaration may be
62 <Emphasis>existentially quantified</Emphasis>. More details in <XRef LinkEnd="existential-quantification">.
68 <Term>Scoped type variables:</Term>
71 Scoped type variables enable the programmer to supply type signatures
72 for some nested declarations, where this would not be legal in Haskell
73 98. Details in <XRef LinkEnd="scoped-type-variables">.
79 <Term>Pattern guards</Term>
82 Instead of being a boolean expression, a guard is a list of qualifiers, exactly as in a list comprehension. See <XRef LinkEnd="pattern-guards">.
88 <Term>Foreign calling:</Term>
91 Just what it sounds like. We provide <Emphasis>lots</Emphasis> of rope that you
92 can dangle around your neck. Please see <XRef LinkEnd="ffi">.
101 Pragmas are special instructions to the compiler placed in the source
102 file. The pragmas GHC supports are described in <XRef LinkEnd="pragmas">.
108 <Term>Rewrite rules:</Term>
111 The programmer can specify rewrite rules as part of the source program
112 (in a pragma). GHC applies these rewrite rules wherever it can.
113 Details in <XRef LinkEnd="rewrite-rules">.
119 <Term>Generic classes:</Term>
122 Generic class declarations allow you to define a class
123 whose methods say how to work over an arbitrary data type.
124 Then it's really easy to make any new type into an instance of
125 the class. This generalises the rather ad-hoc "deriving" feature
127 Details in <XRef LinkEnd="generic-classes">.
135 Before you get too carried away working at the lowest level (e.g.,
136 sloshing <Literal>MutableByteArray#</Literal>s around your
137 program), you may wish to check if there are libraries that provide a
138 “Haskellised veneer” over the features you want. See
139 <xref linkend="book-hslibs">.
142 <Sect1 id="language-options">
143 <Title>Language variations
146 <Para> There are several flags that control what variation of the language are permitted.
147 Leaving out all of them gives you standard Haskell 98.</Para>
152 <Term><Option>-fglasgow-exts</Option>:</Term>
154 <Para>This simultaneously enables all of the extensions to Haskell 98 described in this
155 chapter, except where otherwise noted. </Para>
156 </ListItem> </VarListEntry>
159 <Term><Option>-fno-monomorphism-restriction</Option>:</Term>
161 <Para> Switch off the Haskell 98 monomorphism restriction. Independent of the <Option>-fglasgow-exts</Option>
163 </ListItem> </VarListEntry>
166 <Term><Option>-fallow-overlapping-instances</Option>,
167 <Option>-fallow-undecidable-instances</Option>,
168 <Option>-fcontext-stack</Option>:</Term>
170 <Para> See <XRef LinkEnd="instance-decls">.
171 Only relevant if you also use <Option>-fglasgow-exts</Option>.
173 </ListItem> </VarListEntry>
176 <Term><Option>-fignore-asserts</Option>:</Term>
178 <Para> See <XRef LinkEnd="sec-assertions">.
179 Only relevant if you also use <Option>-fglasgow-exts</Option>.
181 </ListItem> </VarListEntry>
184 <Term> <Option>-finline-phase</Option>:</Term>
186 <Para> See <XRef LinkEnd="rewrite-rules">.
187 Only relevant if you also use <Option>-fglasgow-exts</Option>.
188 </ListItem> </VarListEntry>
191 <Term> <Option>-fgenerics</Option>:</Term>
193 <Para> See <XRef LinkEnd="generic-classes">.
194 Independent of <Option>-fglasgow-exts</Option>.
196 </ListItem> </VarListEntry>
200 <Sect1 id="primitives">
201 <Title>Unboxed types and primitive operations
203 <IndexTerm><Primary>PrelGHC module</Primary></IndexTerm>
206 This module defines all the types which are primitive in Glasgow
207 Haskell, and the operations provided for them.
210 <Sect2 id="glasgow-unboxed">
215 <IndexTerm><Primary>Unboxed types (Glasgow extension)</Primary></IndexTerm>
218 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
219 that values of that type are represented by a pointer to a heap
220 object. The representation of a Haskell <literal>Int</literal>, for
221 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
222 type, however, is represented by the value itself, no pointers or heap
223 allocation are involved.
227 Unboxed types correspond to the “raw machine” types you
228 would use in C: <Literal>Int#</Literal> (long int),
229 <Literal>Double#</Literal> (double), <Literal>Addr#</Literal>
230 (void *), etc. The <Emphasis>primitive operations</Emphasis>
231 (PrimOps) on these types are what you might expect; e.g.,
232 <Literal>(+#)</Literal> is addition on
233 <Literal>Int#</Literal>s, and is the machine-addition that we all
234 know and love—usually one instruction.
238 Primitive (unboxed) types cannot be defined in Haskell, and are
239 therefore built into the language and compiler. Primitive types are
240 always unlifted; that is, a value of a primitive type cannot be
241 bottom. We use the convention that primitive types, values, and
242 operations have a <Literal>#</Literal> suffix.
246 Primitive values are often represented by a simple bit-pattern, such
247 as <Literal>Int#</Literal>, <Literal>Float#</Literal>,
248 <Literal>Double#</Literal>. But this is not necessarily the case:
249 a primitive value might be represented by a pointer to a
250 heap-allocated object. Examples include
251 <Literal>Array#</Literal>, the type of primitive arrays. A
252 primitive array is heap-allocated because it is too big a value to fit
253 in a register, and would be too expensive to copy around; in a sense,
254 it is accidental that it is represented by a pointer. If a pointer
255 represents a primitive value, then it really does point to that value:
256 no unevaluated thunks, no indirections…nothing can be at the
257 other end of the pointer than the primitive value.
261 There are some restrictions on the use of primitive types, the main
262 one being that you can't pass a primitive value to a polymorphic
263 function or store one in a polymorphic data type. This rules out
264 things like <Literal>[Int#]</Literal> (i.e. lists of primitive
265 integers). The reason for this restriction is that polymorphic
266 arguments and constructor fields are assumed to be pointers: if an
267 unboxed integer is stored in one of these, the garbage collector would
268 attempt to follow it, leading to unpredictable space leaks. Or a
269 <Function>seq</Function> operation on the polymorphic component may
270 attempt to dereference the pointer, with disastrous results. Even
271 worse, the unboxed value might be larger than a pointer
272 (<Literal>Double#</Literal> for instance).
276 Nevertheless, A numerically-intensive program using unboxed types can
277 go a <Emphasis>lot</Emphasis> faster than its “standard”
278 counterpart—we saw a threefold speedup on one example.
283 <Sect2 id="unboxed-tuples">
284 <Title>Unboxed Tuples
288 Unboxed tuples aren't really exported by <Literal>PrelGHC</Literal>,
289 they're available by default with <Option>-fglasgow-exts</Option>. An
290 unboxed tuple looks like this:
302 where <Literal>e_1..e_n</Literal> are expressions of any
303 type (primitive or non-primitive). The type of an unboxed tuple looks
308 Unboxed tuples are used for functions that need to return multiple
309 values, but they avoid the heap allocation normally associated with
310 using fully-fledged tuples. When an unboxed tuple is returned, the
311 components are put directly into registers or on the stack; the
312 unboxed tuple itself does not have a composite representation. Many
313 of the primitive operations listed in this section return unboxed
318 There are some pretty stringent restrictions on the use of unboxed tuples:
327 Unboxed tuple types are subject to the same restrictions as
328 other unboxed types; i.e. they may not be stored in polymorphic data
329 structures or passed to polymorphic functions.
336 Unboxed tuples may only be constructed as the direct result of
337 a function, and may only be deconstructed with a <Literal>case</Literal> expression.
338 eg. the following are valid:
342 f x y = (# x+1, y-1 #)
343 g x = case f x x of { (# a, b #) -> a + b }
347 but the following are invalid:
361 No variable can have an unboxed tuple type. This is illegal:
365 f :: (# Int, Int #) -> (# Int, Int #)
370 because <VarName>x</VarName> has an unboxed tuple type.
380 Note: we may relax some of these restrictions in the future.
384 The <Literal>IO</Literal> and <Literal>ST</Literal> monads use unboxed tuples to avoid unnecessary
385 allocation during sequences of operations.
391 <Title>Character and numeric types</Title>
394 <IndexTerm><Primary>character types, primitive</Primary></IndexTerm>
395 <IndexTerm><Primary>numeric types, primitive</Primary></IndexTerm>
396 <IndexTerm><Primary>integer types, primitive</Primary></IndexTerm>
397 <IndexTerm><Primary>floating point types, primitive</Primary></IndexTerm>
398 There are the following obvious primitive types:
414 <IndexTerm><Primary><literal>Char#</literal></Primary></IndexTerm>
415 <IndexTerm><Primary><literal>Int#</literal></Primary></IndexTerm>
416 <IndexTerm><Primary><literal>Word#</literal></Primary></IndexTerm>
417 <IndexTerm><Primary><literal>Addr#</literal></Primary></IndexTerm>
418 <IndexTerm><Primary><literal>Float#</literal></Primary></IndexTerm>
419 <IndexTerm><Primary><literal>Double#</literal></Primary></IndexTerm>
420 <IndexTerm><Primary><literal>Int64#</literal></Primary></IndexTerm>
421 <IndexTerm><Primary><literal>Word64#</literal></Primary></IndexTerm>
425 If you really want to know their exact equivalents in C, see
426 <Filename>ghc/includes/StgTypes.h</Filename> in the GHC source tree.
430 Literals for these types may be written as follows:
439 'a'# a Char#; for weird characters, use e.g. '\o<octal>'#
440 "a"# an Addr# (a `char *'); only characters '\0'..'\255' allowed
443 <IndexTerm><Primary>literals, primitive</Primary></IndexTerm>
444 <IndexTerm><Primary>constants, primitive</Primary></IndexTerm>
445 <IndexTerm><Primary>numbers, primitive</Primary></IndexTerm>
451 <Title>Comparison operations</Title>
454 <IndexTerm><Primary>comparisons, primitive</Primary></IndexTerm>
455 <IndexTerm><Primary>operators, comparison</Primary></IndexTerm>
461 {>,>=,==,/=,<,<=}# :: Int# -> Int# -> Bool
463 {gt,ge,eq,ne,lt,le}Char# :: Char# -> Char# -> Bool
464 -- ditto for Word# and Addr#
467 <IndexTerm><Primary><literal>>#</literal></Primary></IndexTerm>
468 <IndexTerm><Primary><literal>>=#</literal></Primary></IndexTerm>
469 <IndexTerm><Primary><literal>==#</literal></Primary></IndexTerm>
470 <IndexTerm><Primary><literal>/=#</literal></Primary></IndexTerm>
471 <IndexTerm><Primary><literal><#</literal></Primary></IndexTerm>
472 <IndexTerm><Primary><literal><=#</literal></Primary></IndexTerm>
473 <IndexTerm><Primary><literal>gt{Char,Word,Addr}#</literal></Primary></IndexTerm>
474 <IndexTerm><Primary><literal>ge{Char,Word,Addr}#</literal></Primary></IndexTerm>
475 <IndexTerm><Primary><literal>eq{Char,Word,Addr}#</literal></Primary></IndexTerm>
476 <IndexTerm><Primary><literal>ne{Char,Word,Addr}#</literal></Primary></IndexTerm>
477 <IndexTerm><Primary><literal>lt{Char,Word,Addr}#</literal></Primary></IndexTerm>
478 <IndexTerm><Primary><literal>le{Char,Word,Addr}#</literal></Primary></IndexTerm>
484 <Title>Primitive-character operations</Title>
487 <IndexTerm><Primary>characters, primitive operations</Primary></IndexTerm>
488 <IndexTerm><Primary>operators, primitive character</Primary></IndexTerm>
494 ord# :: Char# -> Int#
495 chr# :: Int# -> Char#
498 <IndexTerm><Primary><literal>ord#</literal></Primary></IndexTerm>
499 <IndexTerm><Primary><literal>chr#</literal></Primary></IndexTerm>
505 <Title>Primitive-<Literal>Int</Literal> operations</Title>
508 <IndexTerm><Primary>integers, primitive operations</Primary></IndexTerm>
509 <IndexTerm><Primary>operators, primitive integer</Primary></IndexTerm>
515 {+,-,*,quotInt,remInt,gcdInt}# :: Int# -> Int# -> Int#
516 negateInt# :: Int# -> Int#
518 iShiftL#, iShiftRA#, iShiftRL# :: Int# -> Int# -> Int#
519 -- shift left, right arithmetic, right logical
521 addIntC#, subIntC#, mulIntC# :: Int# -> Int# -> (# Int#, Int# #)
522 -- add, subtract, multiply with carry
525 <IndexTerm><Primary><literal>+#</literal></Primary></IndexTerm>
526 <IndexTerm><Primary><literal>-#</literal></Primary></IndexTerm>
527 <IndexTerm><Primary><literal>*#</literal></Primary></IndexTerm>
528 <IndexTerm><Primary><literal>quotInt#</literal></Primary></IndexTerm>
529 <IndexTerm><Primary><literal>remInt#</literal></Primary></IndexTerm>
530 <IndexTerm><Primary><literal>gcdInt#</literal></Primary></IndexTerm>
531 <IndexTerm><Primary><literal>iShiftL#</literal></Primary></IndexTerm>
532 <IndexTerm><Primary><literal>iShiftRA#</literal></Primary></IndexTerm>
533 <IndexTerm><Primary><literal>iShiftRL#</literal></Primary></IndexTerm>
534 <IndexTerm><Primary><literal>addIntC#</literal></Primary></IndexTerm>
535 <IndexTerm><Primary><literal>subIntC#</literal></Primary></IndexTerm>
536 <IndexTerm><Primary><literal>mulIntC#</literal></Primary></IndexTerm>
537 <IndexTerm><Primary>shift operations, integer</Primary></IndexTerm>
541 <Emphasis>Note:</Emphasis> No error/overflow checking!
547 <Title>Primitive-<Literal>Double</Literal> and <Literal>Float</Literal> operations</Title>
550 <IndexTerm><Primary>floating point numbers, primitive</Primary></IndexTerm>
551 <IndexTerm><Primary>operators, primitive floating point</Primary></IndexTerm>
557 {+,-,*,/}## :: Double# -> Double# -> Double#
558 {<,<=,==,/=,>=,>}## :: Double# -> Double# -> Bool
559 negateDouble# :: Double# -> Double#
560 double2Int# :: Double# -> Int#
561 int2Double# :: Int# -> Double#
563 {plus,minux,times,divide}Float# :: Float# -> Float# -> Float#
564 {gt,ge,eq,ne,lt,le}Float# :: Float# -> Float# -> Bool
565 negateFloat# :: Float# -> Float#
566 float2Int# :: Float# -> Int#
567 int2Float# :: Int# -> Float#
573 <IndexTerm><Primary><literal>+##</literal></Primary></IndexTerm>
574 <IndexTerm><Primary><literal>-##</literal></Primary></IndexTerm>
575 <IndexTerm><Primary><literal>*##</literal></Primary></IndexTerm>
576 <IndexTerm><Primary><literal>/##</literal></Primary></IndexTerm>
577 <IndexTerm><Primary><literal><##</literal></Primary></IndexTerm>
578 <IndexTerm><Primary><literal><=##</literal></Primary></IndexTerm>
579 <IndexTerm><Primary><literal>==##</literal></Primary></IndexTerm>
580 <IndexTerm><Primary><literal>=/##</literal></Primary></IndexTerm>
581 <IndexTerm><Primary><literal>>=##</literal></Primary></IndexTerm>
582 <IndexTerm><Primary><literal>>##</literal></Primary></IndexTerm>
583 <IndexTerm><Primary><literal>negateDouble#</literal></Primary></IndexTerm>
584 <IndexTerm><Primary><literal>double2Int#</literal></Primary></IndexTerm>
585 <IndexTerm><Primary><literal>int2Double#</literal></Primary></IndexTerm>
589 <IndexTerm><Primary><literal>plusFloat#</literal></Primary></IndexTerm>
590 <IndexTerm><Primary><literal>minusFloat#</literal></Primary></IndexTerm>
591 <IndexTerm><Primary><literal>timesFloat#</literal></Primary></IndexTerm>
592 <IndexTerm><Primary><literal>divideFloat#</literal></Primary></IndexTerm>
593 <IndexTerm><Primary><literal>gtFloat#</literal></Primary></IndexTerm>
594 <IndexTerm><Primary><literal>geFloat#</literal></Primary></IndexTerm>
595 <IndexTerm><Primary><literal>eqFloat#</literal></Primary></IndexTerm>
596 <IndexTerm><Primary><literal>neFloat#</literal></Primary></IndexTerm>
597 <IndexTerm><Primary><literal>ltFloat#</literal></Primary></IndexTerm>
598 <IndexTerm><Primary><literal>leFloat#</literal></Primary></IndexTerm>
599 <IndexTerm><Primary><literal>negateFloat#</literal></Primary></IndexTerm>
600 <IndexTerm><Primary><literal>float2Int#</literal></Primary></IndexTerm>
601 <IndexTerm><Primary><literal>int2Float#</literal></Primary></IndexTerm>
605 And a full complement of trigonometric functions:
611 expDouble# :: Double# -> Double#
612 logDouble# :: Double# -> Double#
613 sqrtDouble# :: Double# -> Double#
614 sinDouble# :: Double# -> Double#
615 cosDouble# :: Double# -> Double#
616 tanDouble# :: Double# -> Double#
617 asinDouble# :: Double# -> Double#
618 acosDouble# :: Double# -> Double#
619 atanDouble# :: Double# -> Double#
620 sinhDouble# :: Double# -> Double#
621 coshDouble# :: Double# -> Double#
622 tanhDouble# :: Double# -> Double#
623 powerDouble# :: Double# -> Double# -> Double#
626 <IndexTerm><Primary>trigonometric functions, primitive</Primary></IndexTerm>
630 similarly for <Literal>Float#</Literal>.
634 There are two coercion functions for <Literal>Float#</Literal>/<Literal>Double#</Literal>:
640 float2Double# :: Float# -> Double#
641 double2Float# :: Double# -> Float#
644 <IndexTerm><Primary><literal>float2Double#</literal></Primary></IndexTerm>
645 <IndexTerm><Primary><literal>double2Float#</literal></Primary></IndexTerm>
649 The primitive version of <Function>decodeDouble</Function>
650 (<Function>encodeDouble</Function> is implemented as an external C
657 decodeDouble# :: Double# -> PrelNum.ReturnIntAndGMP
660 <IndexTerm><Primary><literal>encodeDouble#</literal></Primary></IndexTerm>
661 <IndexTerm><Primary><literal>decodeDouble#</literal></Primary></IndexTerm>
665 (And the same for <Literal>Float#</Literal>s.)
670 <Sect2 id="integer-operations">
671 <Title>Operations on/for <Literal>Integers</Literal> (interface to GMP)
675 <IndexTerm><Primary>arbitrary precision integers</Primary></IndexTerm>
676 <IndexTerm><Primary>Integer, operations on</Primary></IndexTerm>
680 We implement <Literal>Integers</Literal> (arbitrary-precision
681 integers) using the GNU multiple-precision (GMP) package (version
686 The data type for <Literal>Integer</Literal> is either a small
687 integer, represented by an <Literal>Int</Literal>, or a large integer
688 represented using the pieces required by GMP's
689 <Literal>MP_INT</Literal> in <Filename>gmp.h</Filename> (see
690 <Filename>gmp.info</Filename> in
691 <Filename>ghc/includes/runtime/gmp</Filename>). It comes out as:
697 data Integer = S# Int# -- small integers
698 | J# Int# ByteArray# -- large integers
701 <IndexTerm><Primary>Integer type</Primary></IndexTerm> The primitive
702 ops to support large <Literal>Integers</Literal> use the
703 “pieces” of the representation, and are as follows:
709 negateInteger# :: Int# -> ByteArray# -> Integer
711 {plus,minus,times}Integer#, gcdInteger#,
712 quotInteger#, remInteger#, divExactInteger#
713 :: Int# -> ByteArray#
714 -> Int# -> ByteArray#
715 -> (# Int#, ByteArray# #)
718 :: Int# -> ByteArray#
719 -> Int# -> ByteArray#
720 -> Int# -- -1 for <; 0 for ==; +1 for >
723 :: Int# -> ByteArray#
725 -> Int# -- -1 for <; 0 for ==; +1 for >
728 :: Int# -> ByteArray#
732 divModInteger#, quotRemInteger#
733 :: Int# -> ByteArray#
734 -> Int# -> ByteArray#
735 -> (# Int#, ByteArray#,
738 integer2Int# :: Int# -> ByteArray# -> Int#
740 int2Integer# :: Int# -> Integer -- NB: no error-checking on these two!
741 word2Integer# :: Word# -> Integer
743 addr2Integer# :: Addr# -> Integer
744 -- the Addr# is taken to be a `char *' string
745 -- to be converted into an Integer.
748 <IndexTerm><Primary><literal>negateInteger#</literal></Primary></IndexTerm>
749 <IndexTerm><Primary><literal>plusInteger#</literal></Primary></IndexTerm>
750 <IndexTerm><Primary><literal>minusInteger#</literal></Primary></IndexTerm>
751 <IndexTerm><Primary><literal>timesInteger#</literal></Primary></IndexTerm>
752 <IndexTerm><Primary><literal>quotInteger#</literal></Primary></IndexTerm>
753 <IndexTerm><Primary><literal>remInteger#</literal></Primary></IndexTerm>
754 <IndexTerm><Primary><literal>gcdInteger#</literal></Primary></IndexTerm>
755 <IndexTerm><Primary><literal>gcdIntegerInt#</literal></Primary></IndexTerm>
756 <IndexTerm><Primary><literal>divExactInteger#</literal></Primary></IndexTerm>
757 <IndexTerm><Primary><literal>cmpInteger#</literal></Primary></IndexTerm>
758 <IndexTerm><Primary><literal>divModInteger#</literal></Primary></IndexTerm>
759 <IndexTerm><Primary><literal>quotRemInteger#</literal></Primary></IndexTerm>
760 <IndexTerm><Primary><literal>integer2Int#</literal></Primary></IndexTerm>
761 <IndexTerm><Primary><literal>int2Integer#</literal></Primary></IndexTerm>
762 <IndexTerm><Primary><literal>word2Integer#</literal></Primary></IndexTerm>
763 <IndexTerm><Primary><literal>addr2Integer#</literal></Primary></IndexTerm>
769 <Title>Words and addresses</Title>
772 <IndexTerm><Primary>word, primitive type</Primary></IndexTerm>
773 <IndexTerm><Primary>address, primitive type</Primary></IndexTerm>
774 <IndexTerm><Primary>unsigned integer, primitive type</Primary></IndexTerm>
775 <IndexTerm><Primary>pointer, primitive type</Primary></IndexTerm>
779 A <Literal>Word#</Literal> is used for bit-twiddling operations.
780 It is the same size as an <Literal>Int#</Literal>, but has no sign
781 nor any arithmetic operations.
784 type Word# -- Same size/etc as Int# but *unsigned*
785 type Addr# -- A pointer from outside the "Haskell world" (from C, probably);
786 -- described under "arrays"
789 <IndexTerm><Primary><literal>Word#</literal></Primary></IndexTerm>
790 <IndexTerm><Primary><literal>Addr#</literal></Primary></IndexTerm>
794 <Literal>Word#</Literal>s and <Literal>Addr#</Literal>s have
795 the usual comparison operations. Other
796 unboxed-<Literal>Word</Literal> ops (bit-twiddling and coercions):
802 {gt,ge,eq,ne,lt,le}Word# :: Word# -> Word# -> Bool
804 and#, or#, xor# :: Word# -> Word# -> Word#
807 quotWord#, remWord# :: Word# -> Word# -> Word#
808 -- word (i.e. unsigned) versions are different from int
809 -- versions, so we have to provide these explicitly.
811 not# :: Word# -> Word#
813 shiftL#, shiftRL# :: Word# -> Int# -> Word#
814 -- shift left, right logical
816 int2Word# :: Int# -> Word# -- just a cast, really
817 word2Int# :: Word# -> Int#
820 <IndexTerm><Primary>bit operations, Word and Addr</Primary></IndexTerm>
821 <IndexTerm><Primary><literal>gtWord#</literal></Primary></IndexTerm>
822 <IndexTerm><Primary><literal>geWord#</literal></Primary></IndexTerm>
823 <IndexTerm><Primary><literal>eqWord#</literal></Primary></IndexTerm>
824 <IndexTerm><Primary><literal>neWord#</literal></Primary></IndexTerm>
825 <IndexTerm><Primary><literal>ltWord#</literal></Primary></IndexTerm>
826 <IndexTerm><Primary><literal>leWord#</literal></Primary></IndexTerm>
827 <IndexTerm><Primary><literal>and#</literal></Primary></IndexTerm>
828 <IndexTerm><Primary><literal>or#</literal></Primary></IndexTerm>
829 <IndexTerm><Primary><literal>xor#</literal></Primary></IndexTerm>
830 <IndexTerm><Primary><literal>not#</literal></Primary></IndexTerm>
831 <IndexTerm><Primary><literal>quotWord#</literal></Primary></IndexTerm>
832 <IndexTerm><Primary><literal>remWord#</literal></Primary></IndexTerm>
833 <IndexTerm><Primary><literal>shiftL#</literal></Primary></IndexTerm>
834 <IndexTerm><Primary><literal>shiftRA#</literal></Primary></IndexTerm>
835 <IndexTerm><Primary><literal>shiftRL#</literal></Primary></IndexTerm>
836 <IndexTerm><Primary><literal>int2Word#</literal></Primary></IndexTerm>
837 <IndexTerm><Primary><literal>word2Int#</literal></Primary></IndexTerm>
841 Unboxed-<Literal>Addr</Literal> ops (C casts, really):
844 {gt,ge,eq,ne,lt,le}Addr# :: Addr# -> Addr# -> Bool
846 int2Addr# :: Int# -> Addr#
847 addr2Int# :: Addr# -> Int#
848 addr2Integer# :: Addr# -> (# Int#, ByteArray# #)
851 <IndexTerm><Primary><literal>gtAddr#</literal></Primary></IndexTerm>
852 <IndexTerm><Primary><literal>geAddr#</literal></Primary></IndexTerm>
853 <IndexTerm><Primary><literal>eqAddr#</literal></Primary></IndexTerm>
854 <IndexTerm><Primary><literal>neAddr#</literal></Primary></IndexTerm>
855 <IndexTerm><Primary><literal>ltAddr#</literal></Primary></IndexTerm>
856 <IndexTerm><Primary><literal>leAddr#</literal></Primary></IndexTerm>
857 <IndexTerm><Primary><literal>int2Addr#</literal></Primary></IndexTerm>
858 <IndexTerm><Primary><literal>addr2Int#</literal></Primary></IndexTerm>
859 <IndexTerm><Primary><literal>addr2Integer#</literal></Primary></IndexTerm>
863 The casts between <Literal>Int#</Literal>,
864 <Literal>Word#</Literal> and <Literal>Addr#</Literal>
865 correspond to null operations at the machine level, but are required
866 to keep the Haskell type checker happy.
870 Operations for indexing off of C pointers
871 (<Literal>Addr#</Literal>s) to snatch values are listed under
872 “arrays”.
878 <Title>Arrays</Title>
881 <IndexTerm><Primary>arrays, primitive</Primary></IndexTerm>
885 The type <Literal>Array# elt</Literal> is the type of primitive,
886 unpointed arrays of values of type <Literal>elt</Literal>.
895 <IndexTerm><Primary><literal>Array#</literal></Primary></IndexTerm>
899 <Literal>Array#</Literal> is more primitive than a Haskell
900 array—indeed, the Haskell <Literal>Array</Literal> interface is
901 implemented using <Literal>Array#</Literal>—in that an
902 <Literal>Array#</Literal> is indexed only by
903 <Literal>Int#</Literal>s, starting at zero. It is also more
904 primitive by virtue of being unboxed. That doesn't mean that it isn't
905 a heap-allocated object—of course, it is. Rather, being unboxed
906 means that it is represented by a pointer to the array itself, and not
907 to a thunk which will evaluate to the array (or to bottom). The
908 components of an <Literal>Array#</Literal> are themselves boxed.
912 The type <Literal>ByteArray#</Literal> is similar to
913 <Literal>Array#</Literal>, except that it contains just a string
914 of (non-pointer) bytes.
923 <IndexTerm><Primary><literal>ByteArray#</literal></Primary></IndexTerm>
927 Arrays of these types are useful when a Haskell program wishes to
928 construct a value to pass to a C procedure. It is also possible to use
929 them to build (say) arrays of unboxed characters for internal use in a
930 Haskell program. Given these uses, <Literal>ByteArray#</Literal>
931 is deliberately a bit vague about the type of its components.
932 Operations are provided to extract values of type
933 <Literal>Char#</Literal>, <Literal>Int#</Literal>,
934 <Literal>Float#</Literal>, <Literal>Double#</Literal>, and
935 <Literal>Addr#</Literal> from arbitrary offsets within a
936 <Literal>ByteArray#</Literal>. (For type
937 <Literal>Foo#</Literal>, the $i$th offset gets you the $i$th
938 <Literal>Foo#</Literal>, not the <Literal>Foo#</Literal> at
939 byte-position $i$. Mumble.) (If you want a
940 <Literal>Word#</Literal>, grab an <Literal>Int#</Literal>,
945 Lastly, we have static byte-arrays, of type
946 <Literal>Addr#</Literal> [mentioned previously]. (Remember
947 the duality between arrays and pointers in C.) Arrays of this types
948 are represented by a pointer to an array in the world outside Haskell,
949 so this pointer is not followed by the garbage collector. In other
950 respects they are just like <Literal>ByteArray#</Literal>. They
951 are only needed in order to pass values from C to Haskell.
957 <Title>Reading and writing</Title>
960 Primitive arrays are linear, and indexed starting at zero.
964 The size and indices of a <Literal>ByteArray#</Literal>, <Literal>Addr#</Literal>, and
965 <Literal>MutableByteArray#</Literal> are all in bytes. It's up to the program to
966 calculate the correct byte offset from the start of the array. This
967 allows a <Literal>ByteArray#</Literal> to contain a mixture of values of different
968 type, which is often needed when preparing data for and unpicking
969 results from C. (Umm…not true of indices…WDP 95/09)
973 <Emphasis>Should we provide some <Literal>sizeOfDouble#</Literal> constants?</Emphasis>
977 Out-of-range errors on indexing should be caught by the code which
978 uses the primitive operation; the primitive operations themselves do
979 <Emphasis>not</Emphasis> check for out-of-range indexes. The intention is that the
980 primitive ops compile to one machine instruction or thereabouts.
984 We use the terms “reading” and “writing” to refer to accessing
985 <Emphasis>mutable</Emphasis> arrays (see <XRef LinkEnd="sect-mutable">), and
986 “indexing” to refer to reading a value from an <Emphasis>immutable</Emphasis>
991 Immutable byte arrays are straightforward to index (all indices in bytes):
994 indexCharArray# :: ByteArray# -> Int# -> Char#
995 indexIntArray# :: ByteArray# -> Int# -> Int#
996 indexAddrArray# :: ByteArray# -> Int# -> Addr#
997 indexFloatArray# :: ByteArray# -> Int# -> Float#
998 indexDoubleArray# :: ByteArray# -> Int# -> Double#
1000 indexCharOffAddr# :: Addr# -> Int# -> Char#
1001 indexIntOffAddr# :: Addr# -> Int# -> Int#
1002 indexFloatOffAddr# :: Addr# -> Int# -> Float#
1003 indexDoubleOffAddr# :: Addr# -> Int# -> Double#
1004 indexAddrOffAddr# :: Addr# -> Int# -> Addr#
1005 -- Get an Addr# from an Addr# offset
1008 <IndexTerm><Primary><literal>indexCharArray#</literal></Primary></IndexTerm>
1009 <IndexTerm><Primary><literal>indexIntArray#</literal></Primary></IndexTerm>
1010 <IndexTerm><Primary><literal>indexAddrArray#</literal></Primary></IndexTerm>
1011 <IndexTerm><Primary><literal>indexFloatArray#</literal></Primary></IndexTerm>
1012 <IndexTerm><Primary><literal>indexDoubleArray#</literal></Primary></IndexTerm>
1013 <IndexTerm><Primary><literal>indexCharOffAddr#</literal></Primary></IndexTerm>
1014 <IndexTerm><Primary><literal>indexIntOffAddr#</literal></Primary></IndexTerm>
1015 <IndexTerm><Primary><literal>indexFloatOffAddr#</literal></Primary></IndexTerm>
1016 <IndexTerm><Primary><literal>indexDoubleOffAddr#</literal></Primary></IndexTerm>
1017 <IndexTerm><Primary><literal>indexAddrOffAddr#</literal></Primary></IndexTerm>
1021 The last of these, <Function>indexAddrOffAddr#</Function>, extracts an <Literal>Addr#</Literal> using an offset
1022 from another <Literal>Addr#</Literal>, thereby providing the ability to follow a chain of
1027 Something a bit more interesting goes on when indexing arrays of boxed
1028 objects, because the result is simply the boxed object. So presumably
1029 it should be entered—we never usually return an unevaluated
1030 object! This is a pain: primitive ops aren't supposed to do
1031 complicated things like enter objects. The current solution is to
1032 return a single element unboxed tuple (see <XRef LinkEnd="unboxed-tuples">).
1038 indexArray# :: Array# elt -> Int# -> (# elt #)
1041 <IndexTerm><Primary><literal>indexArray#</literal></Primary></IndexTerm>
1047 <Title>The state type</Title>
1050 <IndexTerm><Primary><literal>state, primitive type</literal></Primary></IndexTerm>
1051 <IndexTerm><Primary><literal>State#</literal></Primary></IndexTerm>
1055 The primitive type <Literal>State#</Literal> represents the state of a state
1056 transformer. It is parameterised on the desired type of state, which
1057 serves to keep states from distinct threads distinct from one another.
1058 But the <Emphasis>only</Emphasis> effect of this parameterisation is in the type
1059 system: all values of type <Literal>State#</Literal> are represented in the same way.
1060 Indeed, they are all represented by nothing at all! The code
1061 generator “knows” to generate no code, and allocate no registers
1062 etc, for primitive states.
1074 The type <Literal>GHC.RealWorld</Literal> is truly opaque: there are no values defined
1075 of this type, and no operations over it. It is “primitive” in that
1076 sense - but it is <Emphasis>not unlifted!</Emphasis> Its only role in life is to be
1077 the type which distinguishes the <Literal>IO</Literal> state transformer.
1091 <Title>State of the world</Title>
1094 A single, primitive, value of type <Literal>State# RealWorld</Literal> is provided.
1100 realWorld# :: State# RealWorld
1103 <IndexTerm><Primary>realWorld# state object</Primary></IndexTerm>
1107 (Note: in the compiler, not a <Literal>PrimOp</Literal>; just a mucho magic
1108 <Literal>Id</Literal>. Exported from <Literal>GHC</Literal>, though).
1113 <Sect2 id="sect-mutable">
1114 <Title>Mutable arrays</Title>
1117 <IndexTerm><Primary>mutable arrays</Primary></IndexTerm>
1118 <IndexTerm><Primary>arrays, mutable</Primary></IndexTerm>
1119 Corresponding to <Literal>Array#</Literal> and <Literal>ByteArray#</Literal>, we have the types of
1120 mutable versions of each. In each case, the representation is a
1121 pointer to a suitable block of (mutable) heap-allocated storage.
1127 type MutableArray# s elt
1128 type MutableByteArray# s
1131 <IndexTerm><Primary><literal>MutableArray#</literal></Primary></IndexTerm>
1132 <IndexTerm><Primary><literal>MutableByteArray#</literal></Primary></IndexTerm>
1136 <Title>Allocation</Title>
1139 <IndexTerm><Primary>mutable arrays, allocation</Primary></IndexTerm>
1140 <IndexTerm><Primary>arrays, allocation</Primary></IndexTerm>
1141 <IndexTerm><Primary>allocation, of mutable arrays</Primary></IndexTerm>
1145 Mutable arrays can be allocated. Only pointer-arrays are initialised;
1146 arrays of non-pointers are filled in by “user code” rather than by
1147 the array-allocation primitive. Reason: only the pointer case has to
1148 worry about GC striking with a partly-initialised array.
1154 newArray# :: Int# -> elt -> State# s -> (# State# s, MutableArray# s elt #)
1156 newCharArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
1157 newIntArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
1158 newAddrArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
1159 newFloatArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
1160 newDoubleArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
1163 <IndexTerm><Primary><literal>newArray#</literal></Primary></IndexTerm>
1164 <IndexTerm><Primary><literal>newCharArray#</literal></Primary></IndexTerm>
1165 <IndexTerm><Primary><literal>newIntArray#</literal></Primary></IndexTerm>
1166 <IndexTerm><Primary><literal>newAddrArray#</literal></Primary></IndexTerm>
1167 <IndexTerm><Primary><literal>newFloatArray#</literal></Primary></IndexTerm>
1168 <IndexTerm><Primary><literal>newDoubleArray#</literal></Primary></IndexTerm>
1172 The size of a <Literal>ByteArray#</Literal> is given in bytes.
1178 <Title>Reading and writing</Title>
1181 <IndexTerm><Primary>arrays, reading and writing</Primary></IndexTerm>
1187 readArray# :: MutableArray# s elt -> Int# -> State# s -> (# State# s, elt #)
1188 readCharArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Char# #)
1189 readIntArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Int# #)
1190 readAddrArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Addr# #)
1191 readFloatArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Float# #)
1192 readDoubleArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Double# #)
1194 writeArray# :: MutableArray# s elt -> Int# -> elt -> State# s -> State# s
1195 writeCharArray# :: MutableByteArray# s -> Int# -> Char# -> State# s -> State# s
1196 writeIntArray# :: MutableByteArray# s -> Int# -> Int# -> State# s -> State# s
1197 writeAddrArray# :: MutableByteArray# s -> Int# -> Addr# -> State# s -> State# s
1198 writeFloatArray# :: MutableByteArray# s -> Int# -> Float# -> State# s -> State# s
1199 writeDoubleArray# :: MutableByteArray# s -> Int# -> Double# -> State# s -> State# s
1202 <IndexTerm><Primary><literal>readArray#</literal></Primary></IndexTerm>
1203 <IndexTerm><Primary><literal>readCharArray#</literal></Primary></IndexTerm>
1204 <IndexTerm><Primary><literal>readIntArray#</literal></Primary></IndexTerm>
1205 <IndexTerm><Primary><literal>readAddrArray#</literal></Primary></IndexTerm>
1206 <IndexTerm><Primary><literal>readFloatArray#</literal></Primary></IndexTerm>
1207 <IndexTerm><Primary><literal>readDoubleArray#</literal></Primary></IndexTerm>
1208 <IndexTerm><Primary><literal>writeArray#</literal></Primary></IndexTerm>
1209 <IndexTerm><Primary><literal>writeCharArray#</literal></Primary></IndexTerm>
1210 <IndexTerm><Primary><literal>writeIntArray#</literal></Primary></IndexTerm>
1211 <IndexTerm><Primary><literal>writeAddrArray#</literal></Primary></IndexTerm>
1212 <IndexTerm><Primary><literal>writeFloatArray#</literal></Primary></IndexTerm>
1213 <IndexTerm><Primary><literal>writeDoubleArray#</literal></Primary></IndexTerm>
1219 <Title>Equality</Title>
1222 <IndexTerm><Primary>arrays, testing for equality</Primary></IndexTerm>
1226 One can take “equality” of mutable arrays. What is compared is the
1227 <Emphasis>name</Emphasis> or reference to the mutable array, not its contents.
1233 sameMutableArray# :: MutableArray# s elt -> MutableArray# s elt -> Bool
1234 sameMutableByteArray# :: MutableByteArray# s -> MutableByteArray# s -> Bool
1237 <IndexTerm><Primary><literal>sameMutableArray#</literal></Primary></IndexTerm>
1238 <IndexTerm><Primary><literal>sameMutableByteArray#</literal></Primary></IndexTerm>
1244 <Title>Freezing mutable arrays</Title>
1247 <IndexTerm><Primary>arrays, freezing mutable</Primary></IndexTerm>
1248 <IndexTerm><Primary>freezing mutable arrays</Primary></IndexTerm>
1249 <IndexTerm><Primary>mutable arrays, freezing</Primary></IndexTerm>
1253 Only unsafe-freeze has a primitive. (Safe freeze is done directly in Haskell
1254 by copying the array and then using <Function>unsafeFreeze</Function>.)
1260 unsafeFreezeArray# :: MutableArray# s elt -> State# s -> (# State# s, Array# s elt #)
1261 unsafeFreezeByteArray# :: MutableByteArray# s -> State# s -> (# State# s, ByteArray# #)
1264 <IndexTerm><Primary><literal>unsafeFreezeArray#</literal></Primary></IndexTerm>
1265 <IndexTerm><Primary><literal>unsafeFreezeByteArray#</literal></Primary></IndexTerm>
1273 <Title>Synchronizing variables (M-vars)</Title>
1276 <IndexTerm><Primary>synchronising variables (M-vars)</Primary></IndexTerm>
1277 <IndexTerm><Primary>M-Vars</Primary></IndexTerm>
1281 Synchronising variables are the primitive type used to implement
1282 Concurrent Haskell's MVars (see the Concurrent Haskell paper for
1283 the operational behaviour of these operations).
1289 type MVar# s elt -- primitive
1291 newMVar# :: State# s -> (# State# s, MVar# s elt #)
1292 takeMVar# :: SynchVar# s elt -> State# s -> (# State# s, elt #)
1293 putMVar# :: SynchVar# s elt -> State# s -> State# s
1296 <IndexTerm><Primary><literal>SynchVar#</literal></Primary></IndexTerm>
1297 <IndexTerm><Primary><literal>newSynchVar#</literal></Primary></IndexTerm>
1298 <IndexTerm><Primary><literal>takeMVar</literal></Primary></IndexTerm>
1299 <IndexTerm><Primary><literal>putMVar</literal></Primary></IndexTerm>
1306 <Sect1 id="glasgow-ST-monad">
1307 <Title>Primitive state-transformer monad
1311 <IndexTerm><Primary>state transformers (Glasgow extensions)</Primary></IndexTerm>
1312 <IndexTerm><Primary>ST monad (Glasgow extension)</Primary></IndexTerm>
1316 This monad underlies our implementation of arrays, mutable and
1317 immutable, and our implementation of I/O, including “C calls”.
1321 The <Literal>ST</Literal> library, which provides access to the
1322 <Function>ST</Function> monad, is described in <xref
1328 <Sect1 id="glasgow-prim-arrays">
1329 <Title>Primitive arrays, mutable and otherwise
1333 <IndexTerm><Primary>primitive arrays (Glasgow extension)</Primary></IndexTerm>
1334 <IndexTerm><Primary>arrays, primitive (Glasgow extension)</Primary></IndexTerm>
1338 GHC knows about quite a few flavours of Large Swathes of Bytes.
1342 First, GHC distinguishes between primitive arrays of (boxed) Haskell
1343 objects (type <Literal>Array# obj</Literal>) and primitive arrays of bytes (type
1344 <Literal>ByteArray#</Literal>).
1348 Second, it distinguishes between…
1352 <Term>Immutable:</Term>
1355 Arrays that do not change (as with “standard” Haskell arrays); you
1356 can only read from them. Obviously, they do not need the care and
1357 attention of the state-transformer monad.
1362 <Term>Mutable:</Term>
1365 Arrays that may be changed or “mutated.” All the operations on them
1366 live within the state-transformer monad and the updates happen
1367 <Emphasis>in-place</Emphasis>.
1372 <Term>“Static” (in C land):</Term>
1375 A C routine may pass an <Literal>Addr#</Literal> pointer back into Haskell land. There
1376 are then primitive operations with which you may merrily grab values
1377 over in C land, by indexing off the “static” pointer.
1382 <Term>“Stable” pointers:</Term>
1385 If, for some reason, you wish to hand a Haskell pointer (i.e.,
1386 <Emphasis>not</Emphasis> an unboxed value) to a C routine, you first make the
1387 pointer “stable,” so that the garbage collector won't forget that it
1388 exists. That is, GHC provides a safe way to pass Haskell pointers to
1393 Please see <XRef LinkEnd="sec-stable-pointers"> for more details.
1398 <Term>“Foreign objects”:</Term>
1401 A “foreign object” is a safe way to pass an external object (a
1402 C-allocated pointer, say) to Haskell and have Haskell do the Right
1403 Thing when it no longer references the object. So, for example, C
1404 could pass a large bitmap over to Haskell and say “please free this
1405 memory when you're done with it.”
1409 Please see <XRef LinkEnd="sec-ForeignObj"> for more details.
1417 The libraries documentatation gives more details on all these
1418 “primitive array” types and the operations on them.
1424 <Sect1 id="pattern-guards">
1425 <Title>Pattern guards</Title>
1428 <IndexTerm><Primary>Pattern guards (Glasgow extension)</Primary></IndexTerm>
1429 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.)
1433 Suppose we have an abstract data type of finite maps, with a
1437 lookup :: FiniteMap -> Int -> Maybe Int
1440 The lookup returns <Function>Nothing</Function> if the supplied key is not in the domain of the mapping, and <Function>(Just v)</Function> otherwise,
1441 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
1445 clunky env var1 var2 | ok1 && ok2 = val1 + val2
1446 | otherwise = var1 + var2
1448 m1 = lookup env var1
1449 m2 = lookup env var2
1450 ok1 = maybeToBool m1
1451 ok2 = maybeToBool m2
1452 val1 = expectJust m1
1453 val2 = expectJust m2
1457 The auxiliary functions are
1461 maybeToBool :: Maybe a -> Bool
1462 maybeToBool (Just x) = True
1463 maybeToBool Nothing = False
1465 expectJust :: Maybe a -> a
1466 expectJust (Just x) = x
1467 expectJust Nothing = error "Unexpected Nothing"
1471 What is <Function>clunky</Function> doing? The guard <Literal>ok1 &&
1472 ok2</Literal> checks that both lookups succeed, using
1473 <Function>maybeToBool</Function> to convert the <Function>Maybe</Function>
1474 types to booleans. The (lazily evaluated) <Function>expectJust</Function>
1475 calls extract the values from the results of the lookups, and binds the
1476 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
1477 respectively. If either lookup fails, then clunky takes the
1478 <Literal>otherwise</Literal> case and returns the sum of its arguments.
1482 This is certainly legal Haskell, but it is a tremendously verbose and
1483 un-obvious way to achieve the desired effect. Arguably, a more direct way
1484 to write clunky would be to use case expressions:
1488 clunky env var1 var1 = case lookup env var1 of
1490 Just val1 -> case lookup env var2 of
1492 Just val2 -> val1 + val2
1498 This is a bit shorter, but hardly better. Of course, we can rewrite any set
1499 of pattern-matching, guarded equations as case expressions; that is
1500 precisely what the compiler does when compiling equations! The reason that
1501 Haskell provides guarded equations is because they allow us to write down
1502 the cases we want to consider, one at a time, independently of each other.
1503 This structure is hidden in the case version. Two of the right-hand sides
1504 are really the same (<Function>fail</Function>), and the whole expression
1505 tends to become more and more indented.
1509 Here is how I would write clunky:
1513 clunky env var1 var1
1514 | Just val1 <- lookup env var1
1515 , Just val2 <- lookup env var2
1517 ...other equations for clunky...
1521 The semantics should be clear enough. The qualifers are matched in order.
1522 For a <Literal><-</Literal> qualifier, which I call a pattern guard, the
1523 right hand side is evaluated and matched against the pattern on the left.
1524 If the match fails then the whole guard fails and the next equation is
1525 tried. If it succeeds, then the appropriate binding takes place, and the
1526 next qualifier is matched, in the augmented environment. Unlike list
1527 comprehensions, however, the type of the expression to the right of the
1528 <Literal><-</Literal> is the same as the type of the pattern to its
1529 left. The bindings introduced by pattern guards scope over all the
1530 remaining guard qualifiers, and over the right hand side of the equation.
1534 Just as with list comprehensions, boolean expressions can be freely mixed
1535 with among the pattern guards. For example:
1546 Haskell's current guards therefore emerge as a special case, in which the
1547 qualifier list has just one element, a boolean expression.
1551 <sect1 id="sec-ffi">
1552 <title>The foreign interface</title>
1554 <para>The foreign interface consists of the following components:</para>
1558 <para>The Foreign Function Interface language specification
1559 (included in this manual, in <xref linkend="ffi">).</para>
1563 <para>The <literal>Foreign</literal> module (see <xref
1564 linkend="sec-Foreign">) collects together several interfaces
1565 which are useful in specifying foreign language
1566 interfaces, including the following:</para>
1570 <para>The <literal>ForeignObj</literal> module (see <xref
1571 linkend="sec-ForeignObj">), for managing pointers from
1572 Haskell into the outside world.</para>
1576 <para>The <literal>StablePtr</literal> module (see <xref
1577 linkend="sec-stable-pointers">), for managing pointers
1578 into Haskell from the outside world.</para>
1582 <para>The <literal>CTypes</literal> module (see <xref
1583 linkend="sec-CTypes">) gives Haskell equivalents for the
1584 standard C datatypes, for use in making Haskell bindings
1585 to existing C libraries.</para>
1589 <para>The <literal>CTypesISO</literal> module (see <xref
1590 linkend="sec-CTypesISO">) gives Haskell equivalents for C
1591 types defined by the ISO C standard.</para>
1595 <para>The <literal>Storable</literal> library, for
1596 primitive marshalling of data types between Haskell and
1597 the foreign language.</para>
1604 <para>The following sections also give some hints and tips on the use
1605 of the foreign function interface in GHC.</para>
1607 <Sect2 id="glasgow-foreign-headers">
1608 <Title>Using function headers
1612 <IndexTerm><Primary>C calls, function headers</Primary></IndexTerm>
1616 When generating C (using the <Option>-fvia-C</Option> directive), one can assist the
1617 C compiler in detecting type errors by using the <Command>-#include</Command> directive
1618 to provide <Filename>.h</Filename> files containing function headers.
1630 void initialiseEFS (HsInt size);
1631 HsInt terminateEFS (void);
1632 HsForeignObj emptyEFS(void);
1633 HsForeignObj updateEFS (HsForeignObj a, HsInt i, HsInt x);
1634 HsInt lookupEFS (HsForeignObj a, HsInt i);
1638 <para>The types <literal>HsInt</literal>,
1639 <literal>HsForeignObj</literal> etc. are described in <xref
1640 linkend="sec-mapping-table">.</Para>
1642 <Para>Note that this approach is only
1643 <Emphasis>essential</Emphasis> for returning
1644 <Literal>float</Literal>s (or if <Literal>sizeof(int) !=
1645 sizeof(int *)</Literal> on your architecture) but is a Good
1646 Thing for anyone who cares about writing solid code. You're
1647 crazy not to do it.</Para>
1653 <Sect1 id="multi-param-type-classes">
1654 <Title>Multi-parameter type classes
1658 This section documents GHC's implementation of multi-parameter type
1659 classes. There's lots of background in the paper <ULink
1660 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1661 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
1662 Jones, Erik Meijer).
1666 I'd like to thank people who reported shorcomings in the GHC 3.02
1667 implementation. Our default decisions were all conservative ones, and
1668 the experience of these heroic pioneers has given useful concrete
1669 examples to support several generalisations. (These appear below as
1670 design choices not implemented in 3.02.)
1674 I've discussed these notes with Mark Jones, and I believe that Hugs
1675 will migrate towards the same design choices as I outline here.
1676 Thanks to him, and to many others who have offered very useful
1681 <Title>Types</Title>
1684 There are the following restrictions on the form of a qualified
1691 forall tv1..tvn (c1, ...,cn) => type
1697 (Here, I write the "foralls" explicitly, although the Haskell source
1698 language omits them; in Haskell 1.4, all the free type variables of an
1699 explicit source-language type signature are universally quantified,
1700 except for the class type variables in a class declaration. However,
1701 in GHC, you can give the foralls if you want. See <XRef LinkEnd="universal-quantification">).
1710 <Emphasis>Each universally quantified type variable
1711 <Literal>tvi</Literal> must be mentioned (i.e. appear free) in <Literal>type</Literal></Emphasis>.
1713 The reason for this is that a value with a type that does not obey
1714 this restriction could not be used without introducing
1715 ambiguity. Here, for example, is an illegal type:
1719 forall a. Eq a => Int
1723 When a value with this type was used, the constraint <Literal>Eq tv</Literal>
1724 would be introduced where <Literal>tv</Literal> is a fresh type variable, and
1725 (in the dictionary-translation implementation) the value would be
1726 applied to a dictionary for <Literal>Eq tv</Literal>. The difficulty is that we
1727 can never know which instance of <Literal>Eq</Literal> to use because we never
1728 get any more information about <Literal>tv</Literal>.
1735 <Emphasis>Every constraint <Literal>ci</Literal> must mention at least one of the
1736 universally quantified type variables <Literal>tvi</Literal></Emphasis>.
1738 For example, this type is OK because <Literal>C a b</Literal> mentions the
1739 universally quantified type variable <Literal>b</Literal>:
1743 forall a. C a b => burble
1747 The next type is illegal because the constraint <Literal>Eq b</Literal> does not
1748 mention <Literal>a</Literal>:
1752 forall a. Eq b => burble
1756 The reason for this restriction is milder than the other one. The
1757 excluded types are never useful or necessary (because the offending
1758 context doesn't need to be witnessed at this point; it can be floated
1759 out). Furthermore, floating them out increases sharing. Lastly,
1760 excluding them is a conservative choice; it leaves a patch of
1761 territory free in case we need it later.
1771 These restrictions apply to all types, whether declared in a type signature
1776 Unlike Haskell 1.4, constraints in types do <Emphasis>not</Emphasis> have to be of
1777 the form <Emphasis>(class type-variables)</Emphasis>. Thus, these type signatures
1784 f :: Eq (m a) => [m a] -> [m a]
1791 This choice recovers principal types, a property that Haskell 1.4 does not have.
1797 <Title>Class declarations</Title>
1805 <Emphasis>Multi-parameter type classes are permitted</Emphasis>. For example:
1809 class Collection c a where
1810 union :: c a -> c a -> c a
1821 <Emphasis>The class hierarchy must be acyclic</Emphasis>. However, the definition
1822 of "acyclic" involves only the superclass relationships. For example,
1828 op :: D b => a -> b -> b
1831 class C a => D a where { ... }
1835 Here, <Literal>C</Literal> is a superclass of <Literal>D</Literal>, but it's OK for a
1836 class operation <Literal>op</Literal> of <Literal>C</Literal> to mention <Literal>D</Literal>. (It
1837 would not be OK for <Literal>D</Literal> to be a superclass of <Literal>C</Literal>.)
1844 <Emphasis>There are no restrictions on the context in a class declaration
1845 (which introduces superclasses), except that the class hierarchy must
1846 be acyclic</Emphasis>. So these class declarations are OK:
1850 class Functor (m k) => FiniteMap m k where
1853 class (Monad m, Monad (t m)) => Transform t m where
1854 lift :: m a -> (t m) a
1863 <Emphasis>In the signature of a class operation, every constraint
1864 must mention at least one type variable that is not a class type
1865 variable</Emphasis>.
1871 class Collection c a where
1872 mapC :: Collection c b => (a->b) -> c a -> c b
1876 is OK because the constraint <Literal>(Collection a b)</Literal> mentions
1877 <Literal>b</Literal>, even though it also mentions the class variable
1878 <Literal>a</Literal>. On the other hand:
1883 op :: Eq a => (a,b) -> (a,b)
1887 is not OK because the constraint <Literal>(Eq a)</Literal> mentions on the class
1888 type variable <Literal>a</Literal>, but not <Literal>b</Literal>. However, any such
1889 example is easily fixed by moving the offending context up to the
1894 class Eq a => C a where
1899 A yet more relaxed rule would allow the context of a class-op signature
1900 to mention only class type variables. However, that conflicts with
1901 Rule 1(b) for types above.
1908 <Emphasis>The type of each class operation must mention <Emphasis>all</Emphasis> of
1909 the class type variables</Emphasis>. For example:
1913 class Coll s a where
1915 insert :: s -> a -> s
1919 is not OK, because the type of <Literal>empty</Literal> doesn't mention
1920 <Literal>a</Literal>. This rule is a consequence of Rule 1(a), above, for
1921 types, and has the same motivation.
1923 Sometimes, offending class declarations exhibit misunderstandings. For
1924 example, <Literal>Coll</Literal> might be rewritten
1928 class Coll s a where
1930 insert :: s a -> a -> s a
1934 which makes the connection between the type of a collection of
1935 <Literal>a</Literal>'s (namely <Literal>(s a)</Literal>) and the element type <Literal>a</Literal>.
1936 Occasionally this really doesn't work, in which case you can split the
1944 class CollE s => Coll s a where
1945 insert :: s -> a -> s
1958 <Sect2 id="instance-decls">
1959 <Title>Instance declarations</Title>
1967 <Emphasis>Instance declarations may not overlap</Emphasis>. The two instance
1972 instance context1 => C type1 where ...
1973 instance context2 => C type2 where ...
1977 "overlap" if <Literal>type1</Literal> and <Literal>type2</Literal> unify
1979 However, if you give the command line option
1980 <Option>-fallow-overlapping-instances</Option><IndexTerm><Primary>-fallow-overlapping-instances
1981 option</Primary></IndexTerm> then two overlapping instance declarations are permitted
1989 EITHER <Literal>type1</Literal> and <Literal>type2</Literal> do not unify
1995 OR <Literal>type2</Literal> is a substitution instance of <Literal>type1</Literal>
1996 (but not identical to <Literal>type1</Literal>)
2009 Notice that these rules
2016 make it clear which instance decl to use
2017 (pick the most specific one that matches)
2024 do not mention the contexts <Literal>context1</Literal>, <Literal>context2</Literal>
2025 Reason: you can pick which instance decl
2026 "matches" based on the type.
2033 Regrettably, GHC doesn't guarantee to detect overlapping instance
2034 declarations if they appear in different modules. GHC can "see" the
2035 instance declarations in the transitive closure of all the modules
2036 imported by the one being compiled, so it can "see" all instance decls
2037 when it is compiling <Literal>Main</Literal>. However, it currently chooses not
2038 to look at ones that can't possibly be of use in the module currently
2039 being compiled, in the interests of efficiency. (Perhaps we should
2040 change that decision, at least for <Literal>Main</Literal>.)
2047 <Emphasis>There are no restrictions on the type in an instance
2048 <Emphasis>head</Emphasis>, except that at least one must not be a type variable</Emphasis>.
2049 The instance "head" is the bit after the "=>" in an instance decl. For
2050 example, these are OK:
2054 instance C Int a where ...
2056 instance D (Int, Int) where ...
2058 instance E [[a]] where ...
2062 Note that instance heads <Emphasis>may</Emphasis> contain repeated type variables.
2063 For example, this is OK:
2067 instance Stateful (ST s) (MutVar s) where ...
2071 The "at least one not a type variable" restriction is to ensure that
2072 context reduction terminates: each reduction step removes one type
2073 constructor. For example, the following would make the type checker
2074 loop if it wasn't excluded:
2078 instance C a => C a where ...
2082 There are two situations in which the rule is a bit of a pain. First,
2083 if one allows overlapping instance declarations then it's quite
2084 convenient to have a "default instance" declaration that applies if
2085 something more specific does not:
2094 Second, sometimes you might want to use the following to get the
2095 effect of a "class synonym":
2099 class (C1 a, C2 a, C3 a) => C a where { }
2101 instance (C1 a, C2 a, C3 a) => C a where { }
2105 This allows you to write shorter signatures:
2117 f :: (C1 a, C2 a, C3 a) => ...
2121 I'm on the lookout for a simple rule that preserves decidability while
2122 allowing these idioms. The experimental flag
2123 <Option>-fallow-undecidable-instances</Option><IndexTerm><Primary>-fallow-undecidable-instances
2124 option</Primary></IndexTerm> lifts this restriction, allowing all the types in an
2125 instance head to be type variables.
2132 <Emphasis>Unlike Haskell 1.4, instance heads may use type
2133 synonyms</Emphasis>. As always, using a type synonym is just shorthand for
2134 writing the RHS of the type synonym definition. For example:
2138 type Point = (Int,Int)
2139 instance C Point where ...
2140 instance C [Point] where ...
2144 is legal. However, if you added
2148 instance C (Int,Int) where ...
2152 as well, then the compiler will complain about the overlapping
2153 (actually, identical) instance declarations. As always, type synonyms
2154 must be fully applied. You cannot, for example, write:
2159 instance Monad P where ...
2163 This design decision is independent of all the others, and easily
2164 reversed, but it makes sense to me.
2171 <Emphasis>The types in an instance-declaration <Emphasis>context</Emphasis> must all
2172 be type variables</Emphasis>. Thus
2176 instance C a b => Eq (a,b) where ...
2184 instance C Int b => Foo b where ...
2188 is not OK. Again, the intent here is to make sure that context
2189 reduction terminates.
2191 Voluminous correspondence on the Haskell mailing list has convinced me
2192 that it's worth experimenting with a more liberal rule. If you use
2193 the flag <Option>-fallow-undecidable-instances</Option> can use arbitrary
2194 types in an instance context. Termination is ensured by having a
2195 fixed-depth recursion stack. If you exceed the stack depth you get a
2196 sort of backtrace, and the opportunity to increase the stack depth
2197 with <Option>-fcontext-stack</Option><Emphasis>N</Emphasis>.
2210 <Sect1 id="universal-quantification">
2211 <Title>Explicit universal quantification
2215 GHC now allows you to write explicitly quantified types. GHC's
2216 syntax for this now agrees with Hugs's, namely:
2222 forall a b. (Ord a, Eq b) => a -> b -> a
2228 The context is, of course, optional. You can't use <Literal>forall</Literal> as
2229 a type variable any more!
2233 Haskell type signatures are implicitly quantified. The <Literal>forall</Literal>
2234 allows us to say exactly what this means. For example:
2252 g :: forall b. (b -> b)
2258 The two are treated identically.
2262 <Title>Universally-quantified data type fields
2266 In a <Literal>data</Literal> or <Literal>newtype</Literal> declaration one can quantify
2267 the types of the constructor arguments. Here are several examples:
2273 data T a = T1 (forall b. b -> b -> b) a
2275 data MonadT m = MkMonad { return :: forall a. a -> m a,
2276 bind :: forall a b. m a -> (a -> m b) -> m b
2279 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2285 The constructors now have so-called <Emphasis>rank 2</Emphasis> polymorphic
2286 types, in which there is a for-all in the argument types.:
2292 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2293 MkMonad :: forall m. (forall a. a -> m a)
2294 -> (forall a b. m a -> (a -> m b) -> m b)
2296 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2302 Notice that you don't need to use a <Literal>forall</Literal> if there's an
2303 explicit context. For example in the first argument of the
2304 constructor <Function>MkSwizzle</Function>, an implicit "<Literal>forall a.</Literal>" is
2305 prefixed to the argument type. The implicit <Literal>forall</Literal>
2306 quantifies all type variables that are not already in scope, and are
2307 mentioned in the type quantified over.
2311 As for type signatures, implicit quantification happens for non-overloaded
2312 types too. So if you write this:
2315 data T a = MkT (Either a b) (b -> b)
2318 it's just as if you had written this:
2321 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2324 That is, since the type variable <Literal>b</Literal> isn't in scope, it's
2325 implicitly universally quantified. (Arguably, it would be better
2326 to <Emphasis>require</Emphasis> explicit quantification on constructor arguments
2327 where that is what is wanted. Feedback welcomed.)
2333 <Title>Construction </Title>
2336 You construct values of types <Literal>T1, MonadT, Swizzle</Literal> by applying
2337 the constructor to suitable values, just as usual. For example,
2343 (T1 (\xy->x) 3) :: T Int
2345 (MkSwizzle sort) :: Swizzle
2346 (MkSwizzle reverse) :: Swizzle
2353 MkMonad r b) :: MonadT Maybe
2359 The type of the argument can, as usual, be more general than the type
2360 required, as <Literal>(MkSwizzle reverse)</Literal> shows. (<Function>reverse</Function>
2361 does not need the <Literal>Ord</Literal> constraint.)
2367 <Title>Pattern matching</Title>
2370 When you use pattern matching, the bound variables may now have
2371 polymorphic types. For example:
2377 f :: T a -> a -> (a, Char)
2378 f (T1 f k) x = (f k x, f 'c' 'd')
2380 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2381 g (MkSwizzle s) xs f = s (map f (s xs))
2383 h :: MonadT m -> [m a] -> m [a]
2384 h m [] = return m []
2385 h m (x:xs) = bind m x $ \y ->
2386 bind m (h m xs) $ \ys ->
2393 In the function <Function>h</Function> we use the record selectors <Literal>return</Literal>
2394 and <Literal>bind</Literal> to extract the polymorphic bind and return functions
2395 from the <Literal>MonadT</Literal> data structure, rather than using pattern
2400 You cannot pattern-match against an argument that is polymorphic.
2404 newtype TIM s a = TIM (ST s (Maybe a))
2406 runTIM :: (forall s. TIM s a) -> Maybe a
2407 runTIM (TIM m) = runST m
2413 Here the pattern-match fails, because you can't pattern-match against
2414 an argument of type <Literal>(forall s. TIM s a)</Literal>. Instead you
2415 must bind the variable and pattern match in the right hand side:
2418 runTIM :: (forall s. TIM s a) -> Maybe a
2419 runTIM tm = case tm of { TIM m -> runST m }
2422 The <Literal>tm</Literal> on the right hand side is (invisibly) instantiated, like
2423 any polymorphic value at its occurrence site, and now you can pattern-match
2430 <Title>The partial-application restriction</Title>
2433 There is really only one way in which data structures with polymorphic
2434 components might surprise you: you must not partially apply them.
2435 For example, this is illegal:
2441 map MkSwizzle [sort, reverse]
2447 The restriction is this: <Emphasis>every subexpression of the program must
2448 have a type that has no for-alls, except that in a function
2449 application (f e1…en) the partial applications are not subject to
2450 this rule</Emphasis>. The restriction makes type inference feasible.
2454 In the illegal example, the sub-expression <Literal>MkSwizzle</Literal> has the
2455 polymorphic type <Literal>(Ord b => [b] -> [b]) -> Swizzle</Literal> and is not
2456 a sub-expression of an enclosing application. On the other hand, this
2463 map (T1 (\a b -> a)) [1,2,3]
2469 even though it involves a partial application of <Function>T1</Function>, because
2470 the sub-expression <Literal>T1 (\a b -> a)</Literal> has type <Literal>Int -> T
2477 <Title>Type signatures
2481 Once you have data constructors with universally-quantified fields, or
2482 constants such as <Constant>runST</Constant> that have rank-2 types, it isn't long
2483 before you discover that you need more! Consider:
2489 mkTs f x y = [T1 f x, T1 f y]
2495 <Function>mkTs</Function> is a fuction that constructs some values of type
2496 <Literal>T</Literal>, using some pieces passed to it. The trouble is that since
2497 <Literal>f</Literal> is a function argument, Haskell assumes that it is
2498 monomorphic, so we'll get a type error when applying <Function>T1</Function> to
2499 it. This is a rather silly example, but the problem really bites in
2500 practice. Lots of people trip over the fact that you can't make
2501 "wrappers functions" for <Constant>runST</Constant> for exactly the same reason.
2502 In short, it is impossible to build abstractions around functions with
2507 The solution is fairly clear. We provide the ability to give a rank-2
2508 type signature for <Emphasis>ordinary</Emphasis> functions (not only data
2509 constructors), thus:
2515 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2516 mkTs f x y = [T1 f x, T1 f y]
2522 This type signature tells the compiler to attribute <Literal>f</Literal> with
2523 the polymorphic type <Literal>(forall b. b -> b -> b)</Literal> when type
2524 checking the body of <Function>mkTs</Function>, so now the application of
2525 <Function>T1</Function> is fine.
2529 There are two restrictions:
2538 You can only define a rank 2 type, specified by the following
2543 rank2type ::= [forall tyvars .] [context =>] funty
2544 funty ::= ([forall tyvars .] [context =>] ty) -> funty
2546 ty ::= ...current Haskell monotype syntax...
2550 Informally, the universal quantification must all be right at the beginning,
2551 or at the top level of a function argument.
2558 There is a restriction on the definition of a function whose
2559 type signature is a rank-2 type: the polymorphic arguments must be
2560 matched on the left hand side of the "<Literal>=</Literal>" sign. You can't
2561 define <Function>mkTs</Function> like this:
2565 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2566 mkTs = \ f x y -> [T1 f x, T1 f y]
2571 The same partial-application rule applies to ordinary functions with
2572 rank-2 types as applied to data constructors.
2585 <Title>Type synonyms and hoisting
2589 GHC also allows you to write a <Literal>forall</Literal> in a type synonym, thus:
2591 type Discard a = forall b. a -> b -> a
2596 However, it is often convenient to use these sort of synonyms at the right hand
2597 end of an arrow, thus:
2599 type Discard a = forall b. a -> b -> a
2601 g :: Int -> Discard Int
2604 Simply expanding the type synonym would give
2606 g :: Int -> (forall b. Int -> b -> Int)
2608 but GHC "hoists" the <Literal>forall</Literal> to give the isomorphic type
2610 g :: forall b. Int -> Int -> b -> Int
2612 In general, the rule is this: <Emphasis>to determine the type specified by any explicit
2613 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2614 performs the transformation:</Emphasis>
2616 <Emphasis>type1</Emphasis> -> forall a. <Emphasis>type2</Emphasis>
2618 forall a. <Emphasis>type1</Emphasis> -> <Emphasis>type2</Emphasis>
2620 (In fact, GHC tries to retain as much synonym information as possible for use in
2621 error messages, but that is a usability issue.) This rule applies, of course, whether
2622 or not the <Literal>forall</Literal> comes from a synonym. For example, here is another
2623 valid way to write <Literal>g</Literal>'s type signature:
2625 g :: Int -> Int -> forall b. b -> Int
2632 <Sect1 id="existential-quantification">
2633 <Title>Existentially quantified data constructors
2637 The idea of using existential quantification in data type declarations
2638 was suggested by Laufer (I believe, thought doubtless someone will
2639 correct me), and implemented in Hope+. It's been in Lennart
2640 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
2641 proved very useful. Here's the idea. Consider the declaration:
2647 data Foo = forall a. MkFoo a (a -> Bool)
2654 The data type <Literal>Foo</Literal> has two constructors with types:
2660 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2667 Notice that the type variable <Literal>a</Literal> in the type of <Function>MkFoo</Function>
2668 does not appear in the data type itself, which is plain <Literal>Foo</Literal>.
2669 For example, the following expression is fine:
2675 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2681 Here, <Literal>(MkFoo 3 even)</Literal> packages an integer with a function
2682 <Function>even</Function> that maps an integer to <Literal>Bool</Literal>; and <Function>MkFoo 'c'
2683 isUpper</Function> packages a character with a compatible function. These
2684 two things are each of type <Literal>Foo</Literal> and can be put in a list.
2688 What can we do with a value of type <Literal>Foo</Literal>?. In particular,
2689 what happens when we pattern-match on <Function>MkFoo</Function>?
2695 f (MkFoo val fn) = ???
2701 Since all we know about <Literal>val</Literal> and <Function>fn</Function> is that they
2702 are compatible, the only (useful) thing we can do with them is to
2703 apply <Function>fn</Function> to <Literal>val</Literal> to get a boolean. For example:
2710 f (MkFoo val fn) = fn val
2716 What this allows us to do is to package heterogenous values
2717 together with a bunch of functions that manipulate them, and then treat
2718 that collection of packages in a uniform manner. You can express
2719 quite a bit of object-oriented-like programming this way.
2722 <Sect2 id="existential">
2723 <Title>Why existential?
2727 What has this to do with <Emphasis>existential</Emphasis> quantification?
2728 Simply that <Function>MkFoo</Function> has the (nearly) isomorphic type
2734 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2740 But Haskell programmers can safely think of the ordinary
2741 <Emphasis>universally</Emphasis> quantified type given above, thereby avoiding
2742 adding a new existential quantification construct.
2748 <Title>Type classes</Title>
2751 An easy extension (implemented in <Command>hbc</Command>) is to allow
2752 arbitrary contexts before the constructor. For example:
2758 data Baz = forall a. Eq a => Baz1 a a
2759 | forall b. Show b => Baz2 b (b -> b)
2765 The two constructors have the types you'd expect:
2771 Baz1 :: forall a. Eq a => a -> a -> Baz
2772 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2778 But when pattern matching on <Function>Baz1</Function> the matched values can be compared
2779 for equality, and when pattern matching on <Function>Baz2</Function> the first matched
2780 value can be converted to a string (as well as applying the function to it).
2781 So this program is legal:
2788 f (Baz1 p q) | p == q = "Yes"
2790 f (Baz1 v fn) = show (fn v)
2796 Operationally, in a dictionary-passing implementation, the
2797 constructors <Function>Baz1</Function> and <Function>Baz2</Function> must store the
2798 dictionaries for <Literal>Eq</Literal> and <Literal>Show</Literal> respectively, and
2799 extract it on pattern matching.
2803 Notice the way that the syntax fits smoothly with that used for
2804 universal quantification earlier.
2810 <Title>Restrictions</Title>
2813 There are several restrictions on the ways in which existentially-quantified
2814 constructors can be use.
2823 When pattern matching, each pattern match introduces a new,
2824 distinct, type for each existential type variable. These types cannot
2825 be unified with any other type, nor can they escape from the scope of
2826 the pattern match. For example, these fragments are incorrect:
2834 Here, the type bound by <Function>MkFoo</Function> "escapes", because <Literal>a</Literal>
2835 is the result of <Function>f1</Function>. One way to see why this is wrong is to
2836 ask what type <Function>f1</Function> has:
2840 f1 :: Foo -> a -- Weird!
2844 What is this "<Literal>a</Literal>" in the result type? Clearly we don't mean
2849 f1 :: forall a. Foo -> a -- Wrong!
2853 The original program is just plain wrong. Here's another sort of error
2857 f2 (Baz1 a b) (Baz1 p q) = a==q
2861 It's ok to say <Literal>a==b</Literal> or <Literal>p==q</Literal>, but
2862 <Literal>a==q</Literal> is wrong because it equates the two distinct types arising
2863 from the two <Function>Baz1</Function> constructors.
2871 You can't pattern-match on an existentially quantified
2872 constructor in a <Literal>let</Literal> or <Literal>where</Literal> group of
2873 bindings. So this is illegal:
2877 f3 x = a==b where { Baz1 a b = x }
2881 You can only pattern-match
2882 on an existentially-quantified constructor in a <Literal>case</Literal> expression or
2883 in the patterns of a function definition.
2885 The reason for this restriction is really an implementation one.
2886 Type-checking binding groups is already a nightmare without
2887 existentials complicating the picture. Also an existential pattern
2888 binding at the top level of a module doesn't make sense, because it's
2889 not clear how to prevent the existentially-quantified type "escaping".
2890 So for now, there's a simple-to-state restriction. We'll see how
2898 You can't use existential quantification for <Literal>newtype</Literal>
2899 declarations. So this is illegal:
2903 newtype T = forall a. Ord a => MkT a
2907 Reason: a value of type <Literal>T</Literal> must be represented as a pair
2908 of a dictionary for <Literal>Ord t</Literal> and a value of type <Literal>t</Literal>.
2909 That contradicts the idea that <Literal>newtype</Literal> should have no
2910 concrete representation. You can get just the same efficiency and effect
2911 by using <Literal>data</Literal> instead of <Literal>newtype</Literal>. If there is no
2912 overloading involved, then there is more of a case for allowing
2913 an existentially-quantified <Literal>newtype</Literal>, because the <Literal>data</Literal>
2914 because the <Literal>data</Literal> version does carry an implementation cost,
2915 but single-field existentially quantified constructors aren't much
2916 use. So the simple restriction (no existential stuff on <Literal>newtype</Literal>)
2917 stands, unless there are convincing reasons to change it.
2925 You can't use <Literal>deriving</Literal> to define instances of a
2926 data type with existentially quantified data constructors.
2928 Reason: in most cases it would not make sense. For example:#
2931 data T = forall a. MkT [a] deriving( Eq )
2934 To derive <Literal>Eq</Literal> in the standard way we would need to have equality
2935 between the single component of two <Function>MkT</Function> constructors:
2939 (MkT a) == (MkT b) = ???
2942 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2943 It's just about possible to imagine examples in which the derived instance
2944 would make sense, but it seems altogether simpler simply to prohibit such
2945 declarations. Define your own instances!
2957 <Sect1 id="sec-assertions">
2959 <IndexTerm><Primary>Assertions</Primary></IndexTerm>
2963 If you want to make use of assertions in your standard Haskell code, you
2964 could define a function like the following:
2970 assert :: Bool -> a -> a
2971 assert False x = error "assertion failed!"
2978 which works, but gives you back a less than useful error message --
2979 an assertion failed, but which and where?
2983 One way out is to define an extended <Function>assert</Function> function which also
2984 takes a descriptive string to include in the error message and
2985 perhaps combine this with the use of a pre-processor which inserts
2986 the source location where <Function>assert</Function> was used.
2990 Ghc offers a helping hand here, doing all of this for you. For every
2991 use of <Function>assert</Function> in the user's source:
2997 kelvinToC :: Double -> Double
2998 kelvinToC k = assert (k >= 0.0) (k+273.15)
3004 Ghc will rewrite this to also include the source location where the
3011 assert pred val ==> assertError "Main.hs|15" pred val
3017 The rewrite is only performed by the compiler when it spots
3018 applications of <Function>Exception.assert</Function>, so you can still define and
3019 use your own versions of <Function>assert</Function>, should you so wish. If not,
3020 import <Literal>Exception</Literal> to make use <Function>assert</Function> in your code.
3024 To have the compiler ignore uses of assert, use the compiler option
3025 <Option>-fignore-asserts</Option>. <IndexTerm><Primary>-fignore-asserts option</Primary></IndexTerm> That is,
3026 expressions of the form <Literal>assert pred e</Literal> will be rewritten to <Literal>e</Literal>.
3030 Assertion failures can be caught, see the documentation for the
3031 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
3037 <Sect1 id="scoped-type-variables">
3038 <Title>Scoped Type Variables
3042 A <Emphasis>pattern type signature</Emphasis> can introduce a <Emphasis>scoped type
3043 variable</Emphasis>. For example
3049 f (xs::[a]) = ys ++ ys
3058 The pattern <Literal>(xs::[a])</Literal> includes a type signature for <VarName>xs</VarName>.
3059 This brings the type variable <Literal>a</Literal> into scope; it scopes over
3060 all the patterns and right hand sides for this equation for <Function>f</Function>.
3061 In particular, it is in scope at the type signature for <VarName>y</VarName>.
3065 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
3066 mentioned in the type signature <Emphasis>that are not in scope</Emphasis> are
3067 implicitly universally quantified. (If there are no type variables in
3068 scope, all type variables mentioned in the signature are universally
3069 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
3070 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
3071 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
3072 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
3073 it becomes possible to do so.
3077 Scoped type variables are implemented in both GHC and Hugs. Where the
3078 implementations differ from the specification below, those differences
3083 So much for the basic idea. Here are the details.
3087 <Title>Scope and implicit quantification</Title>
3095 All the type variables mentioned in the patterns for a single
3096 function definition equation, that are not already in scope,
3097 are brought into scope by the patterns. We describe this set as
3098 the <Emphasis>type variables bound by the equation</Emphasis>.
3105 The type variables thus brought into scope may be mentioned
3106 in ordinary type signatures or pattern type signatures anywhere within
3114 In ordinary type signatures, any type variable mentioned in the
3115 signature that is in scope is <Emphasis>not</Emphasis> universally quantified.
3122 Ordinary type signatures do not bring any new type variables
3123 into scope (except in the type signature itself!). So this is illegal:
3132 It's illegal because <VarName>a</VarName> is not in scope in the body of <Function>f</Function>,
3133 so the ordinary signature <Literal>x::a</Literal> is equivalent to <Literal>x::forall a.a</Literal>;
3134 and that is an incorrect typing.
3141 There is no implicit universal quantification on pattern type
3142 signatures, nor may one write an explicit <Literal>forall</Literal> type in a pattern
3143 type signature. The pattern type signature is a monotype.
3151 The type variables in the head of a <Literal>class</Literal> or <Literal>instance</Literal> declaration
3152 scope over the methods defined in the <Literal>where</Literal> part. For example:
3166 (Not implemented in Hugs yet, Dec 98).
3177 <Title>Polymorphism</Title>
3185 Pattern type signatures are completely orthogonal to ordinary, separate
3186 type signatures. The two can be used independently or together. There is
3187 no scoping associated with the names of the type variables in a separate type signature.
3192 f (xs::[b]) = reverse xs
3201 The function must be polymorphic in the type variables
3202 bound by all its equations. Operationally, the type variables bound
3203 by one equation must not:
3210 Be unified with a type (such as <Literal>Int</Literal>, or <Literal>[a]</Literal>).
3216 Be unified with a type variable free in the environment.
3222 Be unified with each other. (They may unify with the type variables
3223 bound by another equation for the same function, of course.)
3230 For example, the following all fail to type check:
3234 f (x::a) (y::b) = [x,y] -- a unifies with b
3236 g (x::a) = x + 1::Int -- a unifies with Int
3238 h x = let k (y::a) = [x,y] -- a is free in the
3239 in k x -- environment
3241 k (x::a) True = ... -- a unifies with Int
3242 k (x::Int) False = ...
3245 w (x::a) = x -- a unifies with [b]
3254 The pattern-bound type variable may, however, be constrained
3255 by the context of the principal type, thus:
3259 f (x::a) (y::a) = x+y*2
3263 gets the inferred type: <Literal>forall a. Num a => a -> a -> a</Literal>.
3274 <Title>Result type signatures</Title>
3282 The result type of a function can be given a signature,
3287 f (x::a) :: [a] = [x,x,x]
3291 The final <Literal>:: [a]</Literal> after all the patterns gives a signature to the
3292 result type. Sometimes this is the only way of naming the type variable
3297 f :: Int -> [a] -> [a]
3298 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3299 in \xs -> map g (reverse xs `zip` xs)
3311 Result type signatures are not yet implemented in Hugs.
3317 <Title>Pattern signatures on other constructs</Title>
3325 A pattern type signature can be on an arbitrary sub-pattern, not
3330 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3339 Pattern type signatures, including the result part, can be used
3340 in lambda abstractions:
3344 (\ (x::a, y) :: a -> x)
3348 Type variables bound by these patterns must be polymorphic in
3349 the sense defined above.
3354 f1 (x::c) = f1 x -- ok
3355 f2 = \(x::c) -> f2 x -- not ok
3359 Here, <Function>f1</Function> is OK, but <Function>f2</Function> is not, because <VarName>c</VarName> gets unified
3360 with a type variable free in the environment, in this
3361 case, the type of <Function>f2</Function>, which is in the environment when
3362 the lambda abstraction is checked.
3369 Pattern type signatures, including the result part, can be used
3370 in <Literal>case</Literal> expressions:
3374 case e of { (x::a, y) :: a -> x }
3378 The pattern-bound type variables must, as usual,
3379 be polymorphic in the following sense: each case alternative,
3380 considered as a lambda abstraction, must be polymorphic.
3385 case (True,False) of { (x::a, y) -> x }
3389 Even though the context is that of a pair of booleans,
3390 the alternative itself is polymorphic. Of course, it is
3395 case (True,False) of { (x::Bool, y) -> x }
3404 To avoid ambiguity, the type after the “<Literal>::</Literal>” in a result
3405 pattern signature on a lambda or <Literal>case</Literal> must be atomic (i.e. a single
3406 token or a parenthesised type of some sort). To see why,
3407 consider how one would parse this:
3420 Pattern type signatures that bind new type variables
3421 may not be used in pattern bindings at all.
3426 f x = let (y, z::a) = x in ...
3430 But these are OK, because they do not bind fresh type variables:
3434 f1 x = let (y, z::Int) = x in ...
3435 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3439 However a single variable is considered a degenerate function binding,
3440 rather than a degerate pattern binding, so this is permitted, even
3441 though it binds a type variable:
3445 f :: (b->b) = \(x::b) -> x
3454 Such degnerate function bindings do not fall under the monomorphism
3461 g :: a -> a -> Bool = \x y. x==y
3467 Here <Function>g</Function> has type <Literal>forall a. Eq a => a -> a -> Bool</Literal>, just as if
3468 <Function>g</Function> had a separate type signature. Lacking a type signature, <Function>g</Function>
3469 would get a monomorphic type.
3475 <Title>Existentials</Title>
3483 Pattern type signatures can bind existential type variables.
3488 data T = forall a. MkT [a]
3491 f (MkT [t::a]) = MkT t3
3508 <Sect1 id="pragmas">
3513 GHC supports several pragmas, or instructions to the compiler placed
3514 in the source code. Pragmas don't affect the meaning of the program,
3515 but they might affect the efficiency of the generated code.
3518 <Sect2 id="inline-pragma">
3519 <Title>INLINE pragma
3521 <IndexTerm><Primary>INLINE pragma</Primary></IndexTerm>
3522 <IndexTerm><Primary>pragma, INLINE</Primary></IndexTerm></Title>
3525 GHC (with <Option>-O</Option>, as always) tries to inline (or “unfold”)
3526 functions/values that are “small enough,” thus avoiding the call
3527 overhead and possibly exposing other more-wonderful optimisations.
3531 You will probably see these unfoldings (in Core syntax) in your
3536 Normally, if GHC decides a function is “too expensive” to inline, it
3537 will not do so, nor will it export that unfolding for other modules to
3542 The sledgehammer you can bring to bear is the
3543 <Literal>INLINE</Literal><IndexTerm><Primary>INLINE pragma</Primary></IndexTerm> pragma, used thusly:
3546 key_function :: Int -> String -> (Bool, Double)
3548 #ifdef __GLASGOW_HASKELL__
3549 {-# INLINE key_function #-}
3553 (You don't need to do the C pre-processor carry-on unless you're going
3554 to stick the code through HBC—it doesn't like <Literal>INLINE</Literal> pragmas.)
3558 The major effect of an <Literal>INLINE</Literal> pragma is to declare a function's
3559 “cost” to be very low. The normal unfolding machinery will then be
3560 very keen to inline it.
3564 An <Literal>INLINE</Literal> pragma for a function can be put anywhere its type
3565 signature could be put.
3569 <Literal>INLINE</Literal> pragmas are a particularly good idea for the
3570 <Literal>then</Literal>/<Literal>return</Literal> (or <Literal>bind</Literal>/<Literal>unit</Literal>) functions in a monad.
3571 For example, in GHC's own <Literal>UniqueSupply</Literal> monad code, we have:
3574 #ifdef __GLASGOW_HASKELL__
3575 {-# INLINE thenUs #-}
3576 {-# INLINE returnUs #-}
3584 <Sect2 id="noinline-pragma">
3585 <Title>NOINLINE pragma
3589 <IndexTerm><Primary>NOINLINE pragma</Primary></IndexTerm>
3590 <IndexTerm><Primary>pragma, NOINLINE</Primary></IndexTerm>
3594 The <Literal>NOINLINE</Literal> pragma does exactly what you'd expect: it stops the
3595 named function from being inlined by the compiler. You shouldn't ever
3596 need to do this, unless you're very cautious about code size.
3601 <Sect2 id="specialize-pragma">
3602 <Title>SPECIALIZE pragma
3606 <IndexTerm><Primary>SPECIALIZE pragma</Primary></IndexTerm>
3607 <IndexTerm><Primary>pragma, SPECIALIZE</Primary></IndexTerm>
3608 <IndexTerm><Primary>overloading, death to</Primary></IndexTerm>
3612 (UK spelling also accepted.) For key overloaded functions, you can
3613 create extra versions (NB: more code space) specialised to particular
3614 types. Thus, if you have an overloaded function:
3620 hammeredLookup :: Ord key => [(key, value)] -> key -> value
3626 If it is heavily used on lists with <Literal>Widget</Literal> keys, you could
3627 specialise it as follows:
3630 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
3636 To get very fancy, you can also specify a named function to use for
3637 the specialised value, by adding <Literal>= blah</Literal>, as in:
3640 {-# SPECIALIZE hammeredLookup :: ...as before... = blah #-}
3643 It's <Emphasis>Your Responsibility</Emphasis> to make sure that <Function>blah</Function> really
3644 behaves as a specialised version of <Function>hammeredLookup</Function>!!!
3648 NOTE: the <Literal>=blah</Literal> feature isn't implemented in GHC 4.xx.
3652 An example in which the <Literal>= blah</Literal> form will Win Big:
3655 toDouble :: Real a => a -> Double
3656 toDouble = fromRational . toRational
3658 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
3659 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
3662 The <Function>i2d</Function> function is virtually one machine instruction; the
3663 default conversion—via an intermediate <Literal>Rational</Literal>—is obscenely
3664 expensive by comparison.
3668 By using the US spelling, your <Literal>SPECIALIZE</Literal> pragma will work with
3669 HBC, too. Note that HBC doesn't support the <Literal>= blah</Literal> form.
3673 A <Literal>SPECIALIZE</Literal> pragma for a function can be put anywhere its type
3674 signature could be put.
3679 <Sect2 id="specialize-instance-pragma">
3680 <Title>SPECIALIZE instance pragma
3684 <IndexTerm><Primary>SPECIALIZE pragma</Primary></IndexTerm>
3685 <IndexTerm><Primary>overloading, death to</Primary></IndexTerm>
3686 Same idea, except for instance declarations. For example:
3689 instance (Eq a) => Eq (Foo a) where { ... usual stuff ... }
3691 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)] #-}
3694 Compatible with HBC, by the way.
3699 <Sect2 id="line-pragma">
3704 <IndexTerm><Primary>LINE pragma</Primary></IndexTerm>
3705 <IndexTerm><Primary>pragma, LINE</Primary></IndexTerm>
3709 This pragma is similar to C's <Literal>#line</Literal> pragma, and is mainly for use in
3710 automatically generated Haskell code. It lets you specify the line
3711 number and filename of the original code; for example
3717 {-# LINE 42 "Foo.vhs" #-}
3723 if you'd generated the current file from something called <Filename>Foo.vhs</Filename>
3724 and this line corresponds to line 42 in the original. GHC will adjust
3725 its error messages to refer to the line/file named in the <Literal>LINE</Literal>
3732 <Title>RULES pragma</Title>
3735 The RULES pragma lets you specify rewrite rules. It is described in
3736 <XRef LinkEnd="rewrite-rules">.
3743 <Sect1 id="rewrite-rules">
3744 <Title>Rewrite rules
3746 <IndexTerm><Primary>RULES pagma</Primary></IndexTerm>
3747 <IndexTerm><Primary>pragma, RULES</Primary></IndexTerm>
3748 <IndexTerm><Primary>rewrite rules</Primary></IndexTerm></Title>
3751 The programmer can specify rewrite rules as part of the source program
3752 (in a pragma). GHC applies these rewrite rules wherever it can.
3760 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3767 <Title>Syntax</Title>
3770 From a syntactic point of view:
3776 Each rule has a name, enclosed in double quotes. The name itself has
3777 no significance at all. It is only used when reporting how many times the rule fired.
3783 There may be zero or more rules in a <Literal>RULES</Literal> pragma.
3789 Layout applies in a <Literal>RULES</Literal> pragma. Currently no new indentation level
3790 is set, so you must lay out your rules starting in the same column as the
3791 enclosing definitions.
3797 Each variable mentioned in a rule must either be in scope (e.g. <Function>map</Function>),
3798 or bound by the <Literal>forall</Literal> (e.g. <Function>f</Function>, <Function>g</Function>, <Function>xs</Function>). The variables bound by
3799 the <Literal>forall</Literal> are called the <Emphasis>pattern</Emphasis> variables. They are separated
3800 by spaces, just like in a type <Literal>forall</Literal>.
3806 A pattern variable may optionally have a type signature.
3807 If the type of the pattern variable is polymorphic, it <Emphasis>must</Emphasis> have a type signature.
3808 For example, here is the <Literal>foldr/build</Literal> rule:
3811 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3812 foldr k z (build g) = g k z
3815 Since <Function>g</Function> has a polymorphic type, it must have a type signature.
3822 The left hand side of a rule must consist of a top-level variable applied
3823 to arbitrary expressions. For example, this is <Emphasis>not</Emphasis> OK:
3826 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3827 "wrong2" forall f. f True = True
3830 In <Literal>"wrong1"</Literal>, the LHS is not an application; in <Literal>"wrong2"</Literal>, the LHS has a pattern variable
3837 A rule does not need to be in the same module as (any of) the
3838 variables it mentions, though of course they need to be in scope.
3844 Rules are automatically exported from a module, just as instance declarations are.
3855 <Title>Semantics</Title>
3858 From a semantic point of view:
3864 Rules are only applied if you use the <Option>-O</Option> flag.
3870 Rules are regarded as left-to-right rewrite rules.
3871 When GHC finds an expression that is a substitution instance of the LHS
3872 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3873 By "a substitution instance" we mean that the LHS can be made equal to the
3874 expression by substituting for the pattern variables.
3881 The LHS and RHS of a rule are typechecked, and must have the
3889 GHC makes absolutely no attempt to verify that the LHS and RHS
3890 of a rule have the same meaning. That is undecideable in general, and
3891 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3898 GHC makes no attempt to make sure that the rules are confluent or
3899 terminating. For example:
3902 "loop" forall x,y. f x y = f y x
3905 This rule will cause the compiler to go into an infinite loop.
3912 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3918 GHC currently uses a very simple, syntactic, matching algorithm
3919 for matching a rule LHS with an expression. It seeks a substitution
3920 which makes the LHS and expression syntactically equal modulo alpha
3921 conversion. The pattern (rule), but not the expression, is eta-expanded if
3922 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3923 But not beta conversion (that's called higher-order matching).
3927 Matching is carried out on GHC's intermediate language, which includes
3928 type abstractions and applications. So a rule only matches if the
3929 types match too. See <XRef LinkEnd="rule-spec"> below.
3935 GHC keeps trying to apply the rules as it optimises the program.
3936 For example, consider:
3945 The expression <Literal>s (t xs)</Literal> does not match the rule <Literal>"map/map"</Literal>, but GHC
3946 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3947 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3948 not be substituted, and the rule would not fire.
3955 In the earlier phases of compilation, GHC inlines <Emphasis>nothing
3956 that appears on the LHS of a rule</Emphasis>, because once you have substituted
3957 for something you can't match against it (given the simple minded
3958 matching). So if you write the rule
3961 "map/map" forall f,g. map f . map g = map (f.g)
3964 this <Emphasis>won't</Emphasis> match the expression <Literal>map f (map g xs)</Literal>.
3965 It will only match something written with explicit use of ".".
3966 Well, not quite. It <Emphasis>will</Emphasis> match the expression
3972 where <Function>wibble</Function> is defined:
3975 wibble f g = map f . map g
3978 because <Function>wibble</Function> will be inlined (it's small).
3980 Later on in compilation, GHC starts inlining even things on the
3981 LHS of rules, but still leaves the rules enabled. This inlining
3982 policy is controlled by the per-simplification-pass flag <Option>-finline-phase</Option><Emphasis>n</Emphasis>.
3989 All rules are implicitly exported from the module, and are therefore
3990 in force in any module that imports the module that defined the rule, directly
3991 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3992 in force when compiling A.) The situation is very similar to that for instance
4004 <Title>List fusion</Title>
4007 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4008 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4009 intermediate list should be eliminated entirely.
4013 The following are good producers:
4025 Enumerations of <Literal>Int</Literal> and <Literal>Char</Literal> (e.g. <Literal>['a'..'z']</Literal>).
4031 Explicit lists (e.g. <Literal>[True, False]</Literal>)
4037 The cons constructor (e.g <Literal>3:4:[]</Literal>)
4043 <Function>++</Function>
4049 <Function>map</Function>
4055 <Function>filter</Function>
4061 <Function>iterate</Function>, <Function>repeat</Function>
4067 <Function>zip</Function>, <Function>zipWith</Function>
4076 The following are good consumers:
4088 <Function>array</Function> (on its second argument)
4094 <Function>length</Function>
4100 <Function>++</Function> (on its first argument)
4106 <Function>map</Function>
4112 <Function>filter</Function>
4118 <Function>concat</Function>
4124 <Function>unzip</Function>, <Function>unzip2</Function>, <Function>unzip3</Function>, <Function>unzip4</Function>
4130 <Function>zip</Function>, <Function>zipWith</Function> (but on one argument only; if both are good producers, <Function>zip</Function>
4131 will fuse with one but not the other)
4137 <Function>partition</Function>
4143 <Function>head</Function>
4149 <Function>and</Function>, <Function>or</Function>, <Function>any</Function>, <Function>all</Function>
4155 <Function>sequence_</Function>
4161 <Function>msum</Function>
4167 <Function>sortBy</Function>
4176 So, for example, the following should generate no intermediate lists:
4179 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4185 This list could readily be extended; if there are Prelude functions that you use
4186 a lot which are not included, please tell us.
4190 If you want to write your own good consumers or producers, look at the
4191 Prelude definitions of the above functions to see how to do so.
4196 <Sect2 id="rule-spec">
4197 <Title>Specialisation
4201 Rewrite rules can be used to get the same effect as a feature
4202 present in earlier version of GHC:
4205 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4208 This told GHC to use <Function>int8ToInt16</Function> instead of <Function>fromIntegral</Function> whenever
4209 the latter was called with type <Literal>Int8 -> Int16</Literal>. That is, rather than
4210 specialising the original definition of <Function>fromIntegral</Function> the programmer is
4211 promising that it is safe to use <Function>int8ToInt16</Function> instead.
4215 This feature is no longer in GHC. But rewrite rules let you do the
4220 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4224 This slightly odd-looking rule instructs GHC to replace <Function>fromIntegral</Function>
4225 by <Function>int8ToInt16</Function> <Emphasis>whenever the types match</Emphasis>. Speaking more operationally,
4226 GHC adds the type and dictionary applications to get the typed rule
4229 forall (d1::Integral Int8) (d2::Num Int16) .
4230 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4234 this rule does not need to be in the same file as fromIntegral,
4235 unlike the <Literal>SPECIALISE</Literal> pragmas which currently do (so that they
4236 have an original definition available to specialise).
4242 <Title>Controlling what's going on</Title>
4250 Use <Option>-ddump-rules</Option> to see what transformation rules GHC is using.
4256 Use <Option>-ddump-simpl-stats</Option> to see what rules are being fired.
4257 If you add <Option>-dppr-debug</Option> you get a more detailed listing.
4263 The defintion of (say) <Function>build</Function> in <FileName>PrelBase.lhs</FileName> looks llike this:
4266 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4267 {-# INLINE build #-}
4271 Notice the <Literal>INLINE</Literal>! That prevents <Literal>(:)</Literal> from being inlined when compiling
4272 <Literal>PrelBase</Literal>, so that an importing module will “see” the <Literal>(:)</Literal>, and can
4273 match it on the LHS of a rule. <Literal>INLINE</Literal> prevents any inlining happening
4274 in the RHS of the <Literal>INLINE</Literal> thing. I regret the delicacy of this.
4281 In <Filename>ghc/lib/std/PrelBase.lhs</Filename> look at the rules for <Function>map</Function> to
4282 see how to write rules that will do fusion and yet give an efficient
4283 program even if fusion doesn't happen. More rules in <Filename>PrelList.lhs</Filename>.
4295 <Sect1 id="generic-classes">
4296 <Title>Generic classes</Title>
4299 The ideas behind this extension are described in detail in "Derivable type classes",
4300 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4301 An example will give the idea:
4309 fromBin :: [Int] -> (a, [Int])
4311 toBin {| Unit |} Unit = []
4312 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4313 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4314 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4316 fromBin {| Unit |} bs = (Unit, bs)
4317 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4318 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4319 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4320 (y,bs'') = fromBin bs'
4323 This class declaration explains how <Literal>toBin</Literal> and <Literal>fromBin</Literal>
4324 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4325 which are defined thus in the library module <Literal>Generics</Literal>:
4329 data a :+: b = Inl a | Inr b
4330 data a :*: b = a :*: b
4333 Now you can make a data type into an instance of Bin like this:
4335 instance (Bin a, Bin b) => Bin (a,b)
4336 instance Bin a => Bin [a]
4338 That is, just leave off the "where" clasuse. Of course, you can put in the
4339 where clause and over-ride whichever methods you please.
4343 <Title> Using generics </Title>
4344 <Para>To use generics you need to</para>
4347 <Para>Use the <Option>-fgenerics</Option> flag.</Para>
4350 <Para>Import the module <Literal>Generics</Literal> from the
4351 <Literal>lang</Literal> package. This import brings into
4352 scope the data types <Literal>Unit</Literal>,
4353 <Literal>:*:</Literal>, and <Literal>:+:</Literal>. (You
4354 don't need this import if you don't mention these types
4355 explicitly; for example, if you are simply giving instance
4356 declarations.)</Para>
4361 <Sect2> <Title> Changes wrt the paper </Title>
4363 Note that the type constructors <Literal>:+:</Literal> and <Literal>:*:</Literal>
4364 can be written infix (indeed, you can now use
4365 any operator starting in a colon as an infix type constructor). Also note that
4366 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4367 Finally, note that the syntax of the type patterns in the class declaration
4368 uses "<Literal>{|</Literal>" and "<Literal>{|</Literal>" brackets; curly braces
4369 alone would ambiguous when they appear on right hand sides (an extension we
4370 anticipate wanting).
4374 <Sect2> <Title>Terminology and restrictions</Title>
4376 Terminology. A "generic default method" in a class declaration
4377 is one that is defined using type patterns as above.
4378 A "polymorphic default method" is a default method defined as in Haskell 98.
4379 A "generic class declaration" is a class declaration with at least one
4380 generic default method.
4388 Alas, we do not yet implement the stuff about constructor names and
4395 A generic class can have only one parameter; you can't have a generic
4396 multi-parameter class.
4402 A default method must be defined entirely using type patterns, or entirely
4403 without. So this is illegal:
4406 op :: a -> (a, Bool)
4407 op {| Unit |} Unit = (Unit, True)
4410 However it is perfectly OK for some methods of a generic class to have
4411 generic default methods and others to have polymorphic default methods.
4417 The type variable(s) in the type pattern for a generic method declaration
4418 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:
4422 op {| p :*: q |} (x :*: y) = op (x :: p)
4430 The type patterns in a generic default method must take one of the forms:
4436 where "a" and "b" are type variables. Furthermore, all the type patterns for
4437 a single type constructor (<Literal>:*:</Literal>, say) must be identical; they
4438 must use the same type variables. So this is illegal:
4442 op {| a :+: b |} (Inl x) = True
4443 op {| p :+: q |} (Inr y) = False
4445 The type patterns must be identical, even in equations for different methods of the class.
4446 So this too is illegal:
4450 op {| a :*: b |} (Inl x) = True
4453 op {| p :*: q |} (Inr y) = False
4455 (The reason for this restriction is that we gather all the equations for a particular type consructor
4456 into a single generic instance declaration.)
4462 A generic method declaration must give a case for each of the three type constructors.
4468 In an instance declaration for a generic class, the idea is that the compiler
4469 will fill in the methods for you, based on the generic templates. However it can only
4474 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
4479 No constructor of the instance type has unboxed fields.
4483 (Of course, these things can only arise if you are already using GHC extensions.)
4484 However, you can still give an instance declarations for types which break these rules,
4485 provided you give explicit code to override any generic default methods.
4493 The option <Option>-ddump-deriv</Option> dumps incomprehensible stuff giving details of
4494 what the compiler does with generic declarations.
4499 <Sect2> <Title> Another example </Title>
4501 Just to finish with, here's another example I rather like:
4505 nCons {| Unit |} _ = 1
4506 nCons {| a :*: b |} _ = 1
4507 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
4510 tag {| Unit |} _ = 1
4511 tag {| a :*: b |} _ = 1
4512 tag {| a :+: b |} (Inl x) = tag x
4513 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
4520 ;;; Local Variables: ***
4522 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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