/usr/lib/open-axiom/src/algebra/boolean.spad is in open-axiom-source 1.4.1+svn~2626-2ubuntu2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 | --Copyright (c) 1991-2002, The Numerical Algorithms Group Ltd.
--All rights reserved.
--Copyright (C) 2007-2012, Gabriel Dos Reis.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
-- - Redistributions of source code must retain the above copyright
-- notice, this list of conditions and the following disclaimer.
--
-- - Redistributions in binary form must reproduce the above copyright
-- notice, this list of conditions and the following disclaimer in
-- the documentation and/or other materials provided with the
-- distribution.
--
-- - Neither the name of The Numerical Algorithms Group Ltd. nor the
-- names of its contributors may be used to endorse or promote products
-- derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
)abbrev category BOOLE BooleanLogic
++ Author: Gabriel Dos Reis
++ Date Created: April 04, 2010
++ Date Last Modified: April 04, 2010
++ Description:
++ This is the category of Boolean logic structures.
BooleanLogic(): Category == Logic with
not: % -> %
++ \spad{not x} returns the complement or negation of \spad{x}.
and: (%,%) -> %
++ \spad{x and y} returns the conjunction of \spad{x} and \spad{y}.
or: (%,%) -> %
++ \spad{x or y} returns the disjunction of \spad{x} and \spad{y}.
add
not x == ~ x
x and y == x /\ y
x or y == x \/ y
)abbrev category LOGIC Logic
++ Author:
++ Date Created:
++ Date Last Changed: May 27, 2009
++ Basic Operations: ~, /\, \/
++ Related Constructors:
++ Keywords: boolean
++ Description:
++ `Logic' provides the basic operations for lattices,
++ e.g., boolean algebra.
Logic: Category == Type with
~: % -> %
++ ~(x) returns the logical complement of x.
/\: (%, %) -> %
++ \spadignore { /\ }returns the logical `meet', e.g. `and'.
\/: (%, %) -> %
++ \spadignore{ \/ } returns the logical `join', e.g. `or'.
add
x \/ y == ~(~x /\ ~y)
)abbrev domain BOOLEAN Boolean
++ Author: Stephen M. Watt
++ Date Created:
++ Date Last Changed: May 27, 2009
++ Basic Operations: true, false, not, and, or, xor, nand, nor, implies
++ Related Constructors:
++ Keywords: boolean
++ Description: \spadtype{Boolean} is the elementary logic with 2 values:
++ true and false
Boolean(): Join(OrderedFinite, PropositionalLogic, ConvertibleTo InputForm) with
xor : (%, %) -> %
++ xor(a,b) returns the logical exclusive {\em or}
++ of Boolean \spad{a} and b.
nand : (%, %) -> %
++ nand(a,b) returns the logical negation of \spad{a} and b.
nor : (%, %) -> %
++ nor(a,b) returns the logical negation of \spad{a} or b.
== add
import %false: % from Foreign Builtin
import %true: % from Foreign Builtin
import %peq: (%,%) -> Boolean from Foreign Builtin
import %and: (%,%) -> % from Foreign Builtin
import %or: (%,%) -> % from Foreign Builtin
import %not: % -> % from Foreign Builtin
true == %true
false == %false
not b == %not b
~b == %not b
a and b == %and(a,b)
a /\ b == %and(a,b)
a or b == %or(a,b)
a \/ b == %or(a,b)
xor(a, b) == (a => %not b; b)
nor(a, b) == (a => %false; %not b)
nand(a, b) == (a => %not b; %true)
a = b == %peq(a,b)
implies(a, b) == (a => b; %true)
equiv(a,b) == %peq(a, b)
a < b == (b => %not a; %false)
size() == 2
index i ==
even?(i::Integer) => %false
%true
lookup a ==
a => 1
2
random() ==
even?(random()$Integer) => %false
%true
convert(x:%):InputForm ==
x => 'true
'false
coerce(x:%):OutputForm ==
x => 'true
'false
)abbrev category PROPLOG PropositionalLogic
++ Author: Gabriel Dos Reis
++ Date Created: Januray 14, 2008
++ Date Last Modified: May 27, 2009
++ Description: This category declares the connectives of
++ Propositional Logic.
PropositionalLogic(): Category == Join(BooleanLogic,SetCategory) with
true: %
++ true is a logical constant.
false: %
++ false is a logical constant.
implies: (%,%) -> %
++ implies(p,q) returns the logical implication of `q' by `p'.
equiv: (%,%) -> %
++ equiv(p,q) returns the logical equivalence of `p', `q'.
)set mess autoload on
)abbrev domain PROPFRML PropositionalFormula
++ Author: Gabriel Dos Reis
++ Date Created: Januray 14, 2008
++ Date Last Modified: February, 2011
++ Description: This domain implements propositional formula build
++ over a term domain, that itself belongs to PropositionalLogic
PropositionalFormula(T: SetCategory): Public == Private where
Public == Join(PropositionalLogic, CoercibleFrom T) with
isAtom : % -> Maybe T
++ \spad{isAtom f} returns a value \spad{v} such that
++ \spad{v case T} holds if the formula \spad{f} is a term.
isNot : % -> Maybe %
++ \spad{isNot f} returns a value \spad{v} such that
++ \spad{v case %} holds if the formula \spad{f} is a negation.
isAnd : % -> Maybe Pair(%,%)
++ \spad{isAnd f} returns a value \spad{v} such that
++ \spad{v case Pair(%,%)} holds if the formula \spad{f}
++ is a conjunction formula.
isOr : % -> Maybe Pair(%,%)
++ \spad{isOr f} returns a value \spad{v} such that
++ \spad{v case Pair(%,%)} holds if the formula \spad{f}
++ is a disjunction formula.
isImplies : % -> Maybe Pair(%,%)
++ \spad{isImplies f} returns a value \spad{v} such that
++ \spad{v case Pair(%,%)} holds if the formula \spad{f}
++ is an implication formula.
isEquiv : % -> Maybe Pair(%,%)
++ \spad{isEquiv f} returns a value \spad{v} such that
++ \spad{v case Pair(%,%)} holds if the formula \spad{f}
++ is an equivalence formula.
conjunction: (%,%) -> %
++ \spad{conjunction(p,q)} returns a formula denoting the
++ conjunction of \spad{p} and \spad{q}.
disjunction: (%,%) -> %
++ \spad{disjunction(p,q)} returns a formula denoting the
++ disjunction of \spad{p} and \spad{q}.
Private == add
Rep == Union(T, Kernel %)
import Kernel %
import BasicOperator
import KernelFunctions2(Identifier,%)
import List %
-- Local names for proposition logical operators
macro FALSE == '%false
macro TRUE == '%true
macro NOT == '%not
macro AND == '%and
macro OR == '%or
macro IMP == '%implies
macro EQV == '%equiv
-- Return the nesting level of a formula
level(f: %): NonNegativeInteger ==
f' := rep f
f' case T => 0
height f'
-- A term is a formula
coerce(t: T): % ==
per t
false == per constantKernel FALSE
true == per constantKernel TRUE
~ p ==
per kernel(operator(NOT, 1::Arity), [p], 1 + level p)
conjunction(p,q) ==
per kernel(operator(AND, 2), [p, q], 1 + max(level p, level q))
p /\ q == conjunction(p,q)
disjunction(p,q) ==
per kernel(operator(OR, 2), [p, q], 1 + max(level p, level q))
p \/ q == disjunction(p,q)
implies(p,q) ==
per kernel(operator(IMP, 2), [p, q], 1 + max(level p, level q))
equiv(p,q) ==
per kernel(operator(EQV, 2), [p, q], 1 + max(level p, level q))
isAtom f ==
f' := rep f
f' case T => just(f'@T)
nothing
isNot f ==
f' := rep f
f' case Kernel(%) and is?(f', NOT) => just(first argument f')
nothing
isBinaryOperator(f: Kernel %, op: Symbol): Maybe Pair(%, %) ==
not is?(f, op) => nothing
args := argument f
just pair(first args, second args)
isAnd f ==
f' := rep f
f' case Kernel % => isBinaryOperator(f', AND)
nothing
isOr f ==
f' := rep f
f' case Kernel % => isBinaryOperator(f', OR)
nothing
isImplies f ==
f' := rep f
f' case Kernel % => isBinaryOperator(f', IMP)
nothing
isEquiv f ==
f' := rep f
f' case Kernel % => isBinaryOperator(f', EQV)
nothing
-- Unparsing grammar.
--
-- Ideally, the following syntax would the external form
-- Formula:
-- EquivFormula
--
-- EquivFormula:
-- ImpliesFormula
-- ImpliesFormula <=> EquivFormula
--
-- ImpliesFormula:
-- OrFormula
-- OrFormula => ImpliesFormula
--
-- OrFormula:
-- AndFormula
-- AndFormula or OrFormula
--
-- AndFormula
-- NotFormula
-- NotFormula and AndFormula
--
-- NotFormula:
-- PrimaryFormula
-- not NotFormula
--
-- PrimaryFormula:
-- Term
-- ( Formula )
--
-- Note: Since the token '=>' already means a construct different
-- from what we would like to have as a notation for
-- propositional logic, we will output the formula `p => q'
-- as implies(p,q), which looks like a function call.
-- Similarly, we do not have the token `<=>' for logical
-- equivalence; so we unparser `p <=> q' as equiv(p,q).
--
-- So, we modify the nonterminal PrimaryFormula to read
-- PrimaryFormula:
-- Term
-- implies(Formula, Formula)
-- equiv(Formula, Formula)
formula: % -> OutputForm
coerce(p: %): OutputForm ==
formula p
primaryFormula(p: %): OutputForm ==
p' := rep p
p' case T => p'@T::OutputForm
case constantIfCan p' is
c@Identifier => c::OutputForm
otherwise =>
is?(p', IMP) or is?(p', EQV) =>
args := argument p'
elt(operator(p')::OutputForm,
[formula first args, formula second args])$OutputForm
paren(formula p)$OutputForm
notFormula(p: %): OutputForm ==
case isNot p is
f@% => elt(outputForm 'not, [notFormula f])$OutputForm
otherwise => primaryFormula p
andFormula(f: %): OutputForm ==
case isAnd f is
p@Pair(%,%) =>
-- ??? idealy, we should be using `and$OutputForm' but
-- ??? a bug in the compiler currently prevents that.
infix(outputForm 'and, notFormula first p,
andFormula second p)$OutputForm
otherwise => notFormula f
orFormula(f: %): OutputForm ==
case isOr f is
p@Pair(%,%) =>
-- ??? idealy, we should be using `or$OutputForm' but
-- ??? a bug in the compiler currently prevents that.
infix(outputForm 'or, andFormula first p,
orFormula second p)$OutputForm
otherwise => andFormula f
formula f ==
-- Note: this should be equivFormula, but see the explanation above.
orFormula f
)abbrev package PROPFUN1 PropositionalFormulaFunctions1
++ Author: Gabriel Dos Reis
++ Date Created: April 03, 2010
++ Date Last Modified: April 03, 2010
++ Description:
++ This package collects unary functions operating on propositional
++ formulae.
PropositionalFormulaFunctions1(T): Public == Private where
T: SetCategory
Public == Type with
dual: PropositionalFormula T -> PropositionalFormula T
++ \spad{dual f} returns the dual of the proposition \spad{f}.
atoms: PropositionalFormula T -> Set T
++ \spad{atoms f} ++ returns the set of atoms appearing in
++ the formula \spad{f}.
simplify: PropositionalFormula T -> PropositionalFormula T
++ \spad{simplify f} returns a formula logically equivalent
++ to \spad{f} where obvious tautologies have been removed.
Private == add
macro F == PropositionalFormula T
inline Pair(F,F)
dual f ==
f = true$F => false$F
f = false$F => true$F
isAtom f case T => f
(f1 := isNot f) case F => not dual f1
(f2 := isAnd f) case Pair(F,F) =>
disjunction(dual first f2, dual second f2)
(f2 := isOr f) case Pair(F,F) =>
conjunction(dual first f2, dual second f2)
error "formula contains `equiv' or `implies'"
atoms f ==
(t := isAtom f) case T => { t }
(f1 := isNot f) case F => atoms f1
(f2 := isAnd f) case Pair(F,F) =>
union(atoms first f2, atoms second f2)
(f2 := isOr f) case Pair(F,F) =>
union(atoms first f2, atoms second f2)
empty()$Set(T)
-- one-step simplification helper function
simplifyOneStep(f: F): F ==
(f1 := isNot f) case F =>
f1 = true$F => false$F
f1 = false$F => true$F
(f1' := isNot f1) case F => f1' -- assume classical logic
f
(f2 := isAnd f) case Pair(F,F) =>
first f2 = false$F or second f2 = false$F => false$F
first f2 = true$F => second f2
second f2 = true$F => first f2
f
(f2 := isOr f) case Pair(F,F) =>
first f2 = false$F => second f2
second f2 = false$F => first f2
first f2 = true$F or second f2 = true$F => true$F
f
(f2 := isImplies f) case Pair(F,F) =>
first f2 = false$F or second f2 = true$F => true$F
first f2 = true$F => second f2
second f2 = false$F => not first f2
f
(f2 := isEquiv f) case Pair(F,F) =>
first f2 = true$F => second f2
second f2 = true$F => first f2
first f2 = false$F => not second f2
second f2 = false$F => not first f2
f
f
simplify f ==
(f1 := isNot f) case F => simplifyOneStep(not simplify f1)
(f2 := isAnd f) case Pair(F,F) =>
simplifyOneStep(conjunction(simplify first f2, simplify second f2))
(f2 := isOr f) case Pair(F,F) =>
simplifyOneStep(disjunction(simplify first f2, simplify second f2))
(f2 := isImplies f) case Pair(F,F) =>
simplifyOneStep(implies(simplify first f2, simplify second f2))
(f2 := isEquiv f) case Pair(F,F) =>
simplifyOneStep(equiv(simplify first f2, simplify second f2))
f
)abbrev package PROPFUN2 PropositionalFormulaFunctions2
++ Author: Gabriel Dos Reis
++ Date Created: April 03, 2010
++ Date Last Modified: April 03, 2010
++ Description:
++ This package collects binary functions operating on propositional
++ formulae.
PropositionalFormulaFunctions2(S,T): Public == Private where
S: SetCategory
T: SetCategory
Public == Type with
map: (S -> T, PropositionalFormula S) -> PropositionalFormula T
++ \spad{map(f,x)} returns a propositional formula where
++ all atoms in \spad{x} have been replaced by the result
++ of applying the function \spad{f} to them.
Private == add
macro FS == PropositionalFormula S
macro FT == PropositionalFormula T
map(f,x) ==
x = true$FS => true$FT
x = false$FS => false$FT
(t := isAtom x) case S => f(t)::FT
(f1 := isNot x) case FS => not map(f,f1)
(f2 := isAnd x) case Pair(FS,FS) =>
conjunction(map(f,first f2), map(f,second f2))
(f2 := isOr x) case Pair(FS,FS) =>
disjunction(map(f,first f2), map(f,second f2))
(f2 := isImplies x) case Pair(FS,FS) =>
implies(map(f,first f2), map(f,second f2))
(f2 := isEquiv x) case Pair(FS,FS) =>
equiv(map(f,first f2), map(f,second f2))
error "invalid propositional formula"
)abbrev domain KTVLOGIC KleeneTrivalentLogic
++ Author: Gabriel Dos Reis
++ Date Created: September 20, 2008
++ Date Last Modified: January 14, 2012
++ Description:
++ This domain implements Kleene's 3-valued propositional logic.
KleeneTrivalentLogic(): Public == Private where
Public == Join(PropositionalLogic,Finite) with
unknown: % ++ the indefinite `unknown'
case: (%,[| false |]) -> Boolean
++ x case false holds if the value of `x' is `false'
case: (%,[| unknown |]) -> Boolean
++ x case unknown holds if the value of `x' is `unknown'
case: (%,[| true |]) -> Boolean
++ s case true holds if the value of `x' is `true'.
Private == Maybe Boolean add
false == per just(false@Boolean)
unknown == per nothing
true == per just(true@Boolean)
x = y == rep x = rep y
x case true == x = true@%
x case false == x = false@%
x case unknown == x = unknown
not x ==
x case false => true
x case unknown => unknown
false
x and y ==
x case false => false
x case unknown =>
y case false => false
unknown
y
x or y ==
x case false => y
x case true => x
y case true => y
unknown
implies(x,y) ==
x case false => true
x case true => y
y case true => true
unknown
equiv(x,y) ==
x case unknown => x
x case true => y
not y
coerce(x: %): OutputForm ==
case rep x is
y@Boolean => y::OutputForm
otherwise => outputForm 'unknown
size() == 3
index n ==
n > 3 => error "index: argument out of bound"
n = 1 => false
n = 2 => unknown
true
lookup x ==
x = false => 1
x = unknown => 2
3
)abbrev domain IBITS IndexedBits
++ Author: Stephen Watt and Michael Monagan
++ Date Created:
++ July 86
++ Change History:
++ Oct 87
++ Basic Operations: range
++ Related Constructors:
++ Keywords: indexed bits
++ Description: \spadtype{IndexedBits} is a domain to compactly represent
++ large quantities of Boolean data.
IndexedBits(mn:Integer): BitAggregate()
== add
import %2bool: NonNegativeInteger -> Boolean from Foreign Builtin
import %2bit: Boolean -> NonNegativeInteger from Foreign Builtin
import %bitveccopy: % -> % from Foreign Builtin
import %bitveclength: % -> NonNegativeInteger from Foreign Builtin
import %bitvecref: (%,Integer) -> NonNegativeInteger
from Foreign Builtin
import %bitveceq: (%,%) -> Boolean from Foreign Builtin
import %bitveclt: (%,%) -> Boolean from Foreign Builtin
import %bitvecnot: % -> % from Foreign Builtin
import %bitvecand: (%,%) -> % from Foreign Builtin
import %bitvecor: (%,%) -> % from Foreign Builtin
import %bitvecxor: (%,%) -> % from Foreign Builtin
import %bitvector: (NonNegativeInteger,NonNegativeInteger) -> %
from Foreign Builtin
minIndex u == mn
-- range check index of `i' into `v'.
range(v: %, i: Integer): Integer ==
i >= 0 and i < #v => i
error "Index out of range"
coerce(v):OutputForm ==
t:Character := char "1"
f:Character := char "0"
s := new(#v, space()$Character)$String
for i in minIndex(s)..maxIndex(s) for j in mn.. repeat
s.i := if v.j then t else f
s::OutputForm
new(n, b) == %bitvector(n, %2bit(b)$Foreign(Builtin))
empty() == %bitvector(0,0)
copy v == %bitveccopy v
#v == %bitveclength v
v = u == %bitveceq(v,u)
v < u == %bitveclt(v,u)
u and v == (#v=#u => %bitvecand(v,u); map("and",v,u))
u or v == (#v=#u => %bitvecor(v,u); map("or", v,u))
xor(v,u) == (#v=#u => %bitvecxor(v,u); map("xor",v,u))
setelt(v:%, i:Integer, f:Boolean) ==
%2bool %store(%bitvecref(v,range(v,i-mn)),%2bit f)$Foreign(Builtin)
elt(v:%, i:Integer) ==
%2bool %bitvecref(v,range(v,i-mn))
~v == %bitvecnot v
u /\ v == (#v=#u => %bitvecand(v,u); map("and",v,u))
u \/ v == (#v=#u => %bitvecor(v,u); map("or", v,u))
)abbrev domain BITS Bits
++ Author: Stephen M. Watt
++ Date Created:
++ Change History:
++ Basic Operations: And, Not, Or
++ Related Constructors:
++ Keywords: bits
++ Description: \spadtype{Bits} provides logical functions for Indexed Bits.
Bits(): Exports == Implementation where
Exports == BitAggregate() with
bits: (NonNegativeInteger, Boolean) -> %
++ bits(n,b) creates bits with n values of b
Implementation == IndexedBits(1) add
bits(n,b) == new(n,b)
)abbrev domain REF Reference
++ Author: Stephen M. Watt
++ Date Created:
++ Date Last Changed: October 11, 2011
++ Basic Operations: deref, ref, setref, =
++ Related Constructors:
++ Keywords: reference
++ Description: \spadtype{Reference} is for making a changeable instance
++ of something.
Reference(S:Type): SetCategory with
ref : S -> %
++ \spad{ref(s)} creates a reference to the object \spad{s}.
deref : % -> S
++ \spad{deref(r)} returns the object referenced by \spad{r}
setref: (%, S) -> S
++ setref(r,s) reset the reference \spad{r} to refer to \spad{s}
= : (%, %) -> Boolean
++ \spad{a=b} tests if \spad{a} and \spad{b} are equal.
== add
Rep == Record(value: S)
import %peq: (%,%) -> Boolean from Foreign Builtin
p = q == %peq(p,q)
ref v == per [v]
deref p == rep(p).value
setref(p, v) == rep(p).value := v
coerce p ==
obj :=
S has CoercibleTo OutputForm => rep(p).value::OutputForm
'?::OutputForm
prefix('ref::OutputForm, [obj])
|