/usr/lib/open-axiom/src/algebra/op.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 | --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--Copyright (C) 2007-2009, 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.
-- SPAD files for the functional world should be compiled in the
-- following order:
--
-- OP kl expr function
)abbrev domain BOP BasicOperator
++ Basic system operators
++ Author: Manuel Bronstein, Gabriel Dos Reis
++ Date Created: 22 March 1988
++ Date Last Updated: May 09, 2009
++ Description:
++ A basic operator is an object that can be applied to a list of
++ arguments from a set, the result being a kernel over that set.
++ Keywords: operator, kernel.
BasicOperator(): Exports == Implementation where
O ==> OutputForm
P ==> AssociationList(String, None)
L ==> List Record(key:String, entry:None)
SEX ==> InputForm
Exports == Join(OrderedSet, OperatorCategory Symbol) with
properties: $ -> P
++ properties(op) returns the list of all the properties
++ currently attached to op.
copy : $ -> $
++ copy(op) returns a copy of op.
operator : Symbol -> $
++ operator(f) makes f into an operator with arbitrary arity.
operator : (Symbol, NonNegativeInteger) -> $
++ operator(f, n) makes f into an n-ary operator.
operator : (Symbol, Arity) -> $
++ \spad{operator(f, a)} makes \spad{f} into an operator
++ of arity \spad{a}.
nullary? : $ -> Boolean
++ nullary?(op) tests if op is nullary.
unary? : $ -> Boolean
++ unary?(op) tests if op is unary.
nary? : $ -> Boolean
++ nary?(op) tests if op has arbitrary arity.
weight : $ -> NonNegativeInteger
++ weight(op) returns the weight attached to op.
weight : ($, NonNegativeInteger) -> $
++ weight(op, n) attaches the weight n to op.
equality : ($, ($, $) -> Boolean) -> $
++ equality(op, foo?) attaches foo? as the "%equal?" property
++ to op. If op1 and op2 have the same name, and one of them
++ has an "%equal?" property f, then \spad{f(op1, op2)} is called to
++ decide whether op1 and op2 should be considered equal.
comparison : ($, ($, $) -> Boolean) -> $
++ comparison(op, foo?) attaches foo? as the "%less?" property
++ to op. If op1 and op2 have the same name, and one of them
++ has a "%less?" property f, then \spad{f(op1, op2)} is called to
++ decide whether \spad{op1 < op2}.
display : $ -> Maybe(List O -> O)
++ display(op) returns the "%display" property of op if
++ it has one attached, and \spad{nothing} otherwise.
display : ($, List O -> O) -> $
++ display(op, foo) attaches foo as the "%display" property
++ of op. If op has a "%display" property f, then \spad{op(a1,...,an)}
++ gets converted to OutputForm as \spad{f(a1,...,an)}.
display : ($, O -> O) -> $
++ display(op, foo) attaches foo as the "%display" property
++ of op. If op has a "%display" property f, then \spad{op(a)}
++ gets converted to OutputForm as \spad{f(a)}.
++ Argument op must be unary.
input : ($, List SEX -> SEX) -> $
++ input(op, foo) attaches foo as the "%input" property
++ of op. If op has a "%input" property f, then \spad{op(a1,...,an)}
++ gets converted to InputForm as \spad{f(a1,...,an)}.
input : $ -> Maybe(List SEX -> SEX)
++ input(op) returns the "%input" property of op if
++ it has one attached, \spad{nothing} otherwise.
has? : (%, Identifier) -> Boolean
++ \spad{has?(op,p)} tests if property \spad{s} is attached to \spad{op}.
assert : (%, Identifier) -> $
++ \spad{assert(op, p)} attaches property \spad{p} to \spad{op}.
++ Argument op is modified "in place", i.e. no copy is made.
deleteProperty!: ($, String) -> $
++ deleteProperty!(op, s) unattaches property s from op.
++ Argument op is modified "in place", i.e. no copy is made.
deleteProperty!: ($, Identifier) -> $
++ \spad{deleteProperty!(op, p)} unattaches property \spad{p} from
++ \spad{op}. Argument \spad{op} is modified "in place",
++ i.e. no copy is made.
property : ($, String) -> Union(None, "failed")
++ property(op, s) returns the value of property s if
++ it is attached to op, and "failed" otherwise.
property : (%, Identifier) -> Maybe None
++ \spad{property(op, p)} returns the value of property \spad{p} if
++ it is attached to \spad{op}, otherwise \spad{nothing}.
setProperty : ($, String, None) -> $
++ setProperty(op, s, v) attaches property s to op,
++ and sets its value to v.
++ Argument op is modified "in place", i.e. no copy is made.
setProperty : ($, Identifier, None) -> $
++ \spad{setProperty(op, p, v)} attaches property \spad{p} to \spad{op},
++ and sets its value to \spad{v}.
++ Argument \spad{op} is modified "in place", i.e. no copy is made.
setProperties : ($, P) -> $
++ setProperties(op, l) sets the property list of op to l.
++ Argument op is modified "in place", i.e. no copy is made.
Implementation ==> add
-- some internal properties
macro LESS? == '%less?
macro EQUAL? == '%equal?
macro WEIGHT == '%weight
macro DISPLAY == '%display
macro SEXPR == '%input
import Arity
import String
-- if narg < 0 then the operator ahs variable arity.
Rep == Record(opname:Symbol, narg: Arity, props:P)
is?(op, s) == name(op) = s
name op == rep(op).opname
properties op == rep(op).props
setProperties(op, l) ==
rep(op).props := l
op
operator(s: Symbol) == per [s, arbitrary(), table()]
operator(s: Symbol, n: NonNegativeInteger) == per [s, n::Arity, table()]
operator(s: Symbol, a: Arity) == per [s, a, table()]
property(op: %, name: String) == search(name, rep(op).props)
property(op: %, p: Identifier) ==
case search(string p, rep(op).props) is
val@None => just val
otherwise => nothing
assert(op: %, p: Identifier) == setProperty(op, p, NIL$Lisp)
has?(op: %, name: Identifier) == key?(string name, rep(op).props)
weight(op, n) == setProperty(op, WEIGHT, n pretend None)
nullary? op == zero? rep(op).narg
unary? op == one? rep(op).narg
nary? op == arbitrary() = rep(op).narg
equality(op, func) == setProperty(op, EQUAL?, func pretend None)
comparison(op, func) == setProperty(op, LESS?, func pretend None)
display(op:$, f:O -> O) == display(op, f first #1)
deleteProperty!(op: %, name: String) == (remove!(name, properties op); op)
deleteProperty!(op: %, p: Identifier) ==
remove!(string p, properties op)
op
setProperty(op: %, name: String, valu: None) ==
rep(op).props.name := valu
op
setProperty(op: %, p: Identifier, valu: None) ==
rep(op).props.(string p) := valu
op
coerce(op:$):OutputForm == name(op)::OutputForm
input(op:$, f:List SEX -> SEX) == setProperty(op, SEXPR, f pretend None)
display(op:$, f:List O -> O) == setProperty(op, DISPLAY, f pretend None)
display op ==
property(op, DISPLAY) pretend Maybe(List O -> O)
input op ==
property(op, SEXPR) pretend Maybe(List SEX -> SEX)
arity op == rep(op).narg
copy op ==
per [name op, rep(op).narg,
table([[r.key, r.entry] for r in entries(properties op)@L]$L)]
-- property EQUAL? contains a function f: (BOP, BOP) -> Boolean
-- such that f(o1, o2) is true iff o1 = o2
op1 = op2 ==
name(op1) ~= name(op2) => false
rep(op1).narg ~= rep(op2).narg => false
brace(keys properties op1)~=$Set(String) brace(keys properties op2) => false
(func := property(op1, EQUAL?)) case None =>
((func@None) pretend (($, $) -> Boolean)) (op1, op2)
true
-- property WEIGHT allows one to change the ordering around
-- by default, every operator has weigth 1
weight op ==
(w := property(op, WEIGHT)) case nothing => 1
(w@None) pretend NonNegativeInteger
-- property LESS? contains a function f: (BOP, BOP) -> Boolean
-- such that f(o1, o2) is true iff o1 < o2
op1 < op2 ==
(w1 := weight op1) ~= (w2 := weight op2) => w1 < w2
rep(op1).narg ~= rep(op2).narg =>
-- FIXME: Horrible.
(rep(op1).narg pretend SingleInteger) < (rep(op2).narg pretend SingleInteger)
name(op1) ~= name(op2) => name(op1) < name(op2)
n1 := #(k1 := brace(keys(properties op1))$Set(String))
n2 := #(k2 := brace(keys(properties op2))$Set(String))
n1 ~= n2 => n1 < n2
not zero?(n1 := #(d1 := difference(k1, k2))) =>
n1 ~= (n2 := #(d2 := difference(k2, k1))) => n1 < n2
inspect(d1) < inspect(d2)
(func := property(op1, LESS?)) case None =>
((func@None) pretend (($, $) -> Boolean)) (op1, op2)
(func := property(op1, EQUAL?)) case None =>
not(((func@None) pretend (($, $) -> Boolean)) (op1, op2))
false
)abbrev package BOP1 BasicOperatorFunctions1
++ Tools to set/get common properties of operators
++ Author: Manuel Bronstein
++ Date Created: 28 Mar 1988
++ Date Last Updated: 15 May 1990
++ Description:
++ This package exports functions to set some commonly used properties
++ of operators, including properties which contain functions.
++ Keywords: operator.
BasicOperatorFunctions1(A:SetCategory): Exports == Implementation where
OP ==> BasicOperator
Exports ==> with
evaluate : (OP, List A) -> Union(A, "failed")
++ evaluate(op, [a1,...,an]) checks if op has an "%eval"
++ property f. If it has, then \spad{f(a1,...,an)} is returned, and
++ "failed" otherwise.
evaluate : (OP, List A -> A) -> OP
++ evaluate(op, foo) attaches foo as the "%eval" property
++ of op. If op has an "%eval" property f, then applying op
++ to \spad{(a1,...,an)} returns the result of \spad{f(a1,...,an)}.
evaluate : (OP, A -> A) -> OP
++ evaluate(op, foo) attaches foo as the "%eval" property
++ of op. If op has an "%eval" property f, then applying op
++ to a returns the result of \spad{f(a)}. Argument op must be unary.
evaluate : OP -> Union(List A -> A, "failed")
++ evaluate(op) returns the value of the "%eval" property of
++ op if it has one, and "failed" otherwise.
derivative : (OP, List (List A -> A)) -> OP
++ derivative(op, [foo1,...,foon]) attaches [foo1,...,foon] as
++ the "%diff" property of op. If op has an "%diff" property
++ \spad{[f1,...,fn]} then applying a derivation D to \spad{op(a1,...,an)}
++ returns \spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.
derivative : (OP, A -> A) -> OP
++ derivative(op, foo) attaches foo as the "%diff" property
++ of op. If op has an "%diff" property f, then applying a
++ derivation D to op(a) returns \spad{f(a) * D(a)}. Argument op must be unary.
derivative : OP -> Union(List(List A -> A), "failed")
++ derivative(op) returns the value of the "%diff" property of
++ op if it has one, and "failed" otherwise.
constantOperator: A -> OP
++ constantOperator(a) returns a nullary operator op
++ such that \spad{op()} always evaluate to \spad{a}.
constantOpIfCan : OP -> Union(A, "failed")
++ constantOpIfCan(op) returns \spad{a} if op is the constant
++ nullary operator always returning \spad{a}, "failed" otherwise.
Implementation ==> add
macro EVAL == '%eval
macro CONST == '%constant
macro DIFF == '%diff
evaluate(op:OP, func:A -> A) == evaluate(op, func first #1)
evaluate op ==
(func := property(op, EVAL)) case nothing => "failed"
(func@None) pretend (List A -> A)
evaluate(op:OP, args:List A) ==
(func := property(op, EVAL)) case nothing => "failed"
((func@None) pretend (List A -> A)) args
evaluate(op:OP, func:List A -> A) ==
setProperty(op, EVAL, func pretend None)
derivative op ==
(func := property(op, DIFF)) case nothing => "failed"
((func@None) pretend List(List A -> A))
derivative(op:OP, grad:List(List A -> A)) ==
setProperty(op, DIFF, grad pretend None)
derivative(op:OP, f:A -> A) ==
unary? op or nary? op =>
derivative(op, [f first #1]$List(List A -> A))
error "Operator is not unary"
cdisp(a: OutputForm, l: List OutputForm): OutputForm == a
csex(a: InputForm, l: List InputForm): InputForm == a
eqconst?(a: OP, b: OP): Boolean ==
(va := property(a, CONST)) case nothing => not has?(b, CONST)
((vb := property(b, CONST)) case None) and
((va@None) pretend A) = ((vb@None) pretend A)
ltconst?(a: OP, b: OP): Boolean ==
(va := property(a, CONST)) case nothing => has?(b, CONST)
((vb := property(b, CONST)) case None) and
before?((va@None) pretend A, (vb@None) pretend A)
opconst:OP :=
comparison(equality(operator('constant, 0), eqconst?),
ltconst?)
constOp(a: A): OP ==
setProperty(display(copy opconst, cdisp(a::OutputForm, #1)),
CONST, a pretend None)
constantOpIfCan op ==
is?(op,'constant) and
((u := property(op, CONST)) case None) => (u@None) pretend A
"failed"
if A has ConvertibleTo InputForm then
constantOperator a == input(constOp a, csex(convert a, #1))
else
constantOperator a == constOp a
)abbrev package COMMONOP CommonOperators
++ Provides commonly used operators
++ Author: Manuel Bronstein
++ Date Created: 25 Mar 1988
++ Date Last Updated: 2 December 1994
++ Description:
++ This package exports the elementary operators, with some semantics
++ already attached to them. The semantics that is attached here is not
++ dependent on the set in which the operators will be applied.
++ Keywords: operator.
CommonOperators(): Exports == Implementation where
OP ==> BasicOperator
O ==> OutputForm
Exports ==> with
operator: Symbol -> OP
++ operator(s) returns an operator with name s, with the
++ appropriate semantics if s is known. If s is not known,
++ the result has no semantics.
Implementation ==> add
macro POWER == '%power
macro ALGOP == '%alg
macro EVEN == 'even
macro ODD == 'odd
DUMMYVAR ==> "%dummyVar"
dpi : List O -> O
dgamma : List O -> O
dquote : List O -> O
dexp : O -> O
dfact : O -> O
startUp : Boolean -> Void
setDummyVar: (OP, NonNegativeInteger) -> OP
brandNew?:Reference(Boolean) := ref true
opalg := operator('rootOf, 2)$OP
oproot := operator('nthRoot, 2)
oppi := operator('pi, 0)
oplog := operator('log, 1)
opexp := operator('exp, 1)
opabs := operator('abs, 1)
opsin := operator('sin, 1)
opcos := operator('cos, 1)
optan := operator('tan, 1)
opcot := operator('cot, 1)
opsec := operator('sec, 1)
opcsc := operator('csc, 1)
opasin := operator('asin, 1)
opacos := operator('acos, 1)
opatan := operator('atan, 1)
opacot := operator('acot, 1)
opasec := operator('asec, 1)
opacsc := operator('acsc, 1)
opsinh := operator('sinh, 1)
opcosh := operator('cosh, 1)
optanh := operator('tanh, 1)
opcoth := operator('coth, 1)
opsech := operator('sech, 1)
opcsch := operator('csch, 1)
opasinh := operator('asinh, 1)
opacosh := operator('acosh, 1)
opatanh := operator('atanh, 1)
opacoth := operator('acoth, 1)
opasech := operator('asech, 1)
opacsch := operator('acsch, 1)
opbox := operator('%box)$OP
oppren := operator('%paren)$OP
opquote := operator('applyQuote)$OP
opdiff := operator('%diff, 3)
opsi := operator('Si, 1)
opci := operator('Ci, 1)
opei := operator('Ei, 1)
opli := operator('li, 1)
operf := operator('erf, 1)
opli2 := operator('dilog, 1)
opGamma := operator('Gamma, 1)
opGamma2 := operator('Gamma2, 2)
opBeta := operator('Beta, 2)
opdigamma := operator('digamma, 1)
oppolygamma := operator('polygamma, 2)
opBesselJ := operator('besselJ, 2)
opBesselY := operator('besselY, 2)
opBesselI := operator('besselI, 2)
opBesselK := operator('besselK, 2)
opAiryAi := operator('airyAi, 1)
opAiryBi := operator('airyBi , 1)
opint := operator('integral, 3)
opdint := operator('%defint, 5)
opfact := operator('factorial, 1)
opperm := operator('permutation, 2)
opbinom := operator('binomial, 2)
oppow := operator(POWER, 2)
opsum := operator('summation, 3)
opdsum := operator('%defsum, 5)
opprod := operator('product, 3)
opdprod := operator('%defprod, 5)
algop := [oproot, opalg]$List(OP)
rtrigop := [opsin, opcos, optan, opcot, opsec, opcsc,
opasin, opacos, opatan, opacot, opasec, opacsc]
htrigop := [opsinh, opcosh, optanh, opcoth, opsech, opcsch,
opasinh, opacosh, opatanh, opacoth, opasech, opacsch]
trigop := concat(rtrigop, htrigop)
elemop := concat(trigop, [oppi, oplog, opexp])
primop := [opei, opli, opsi, opci, operf, opli2, opint, opdint]
combop := [opfact, opperm, opbinom, oppow,
opsum, opdsum, opprod, opdprod]
specop := [opGamma, opGamma2, opBeta, opdigamma, oppolygamma, opabs,
opBesselJ, opBesselY, opBesselI, opBesselK]
anyop := [oppren, opdiff, opbox, opquote]
allop := concat(concat(concat(concat(concat(
algop,elemop),primop),combop),specop),anyop)
-- odd and even operators, must be maintained current!
evenop := [opcos, opsec, opcosh, opsech, opabs]
oddop := [opsin, opcsc, optan, opcot, opasin, opacsc, opatan,
opsinh, opcsch, optanh, opcoth, opasinh, opacsch,opatanh,opacoth,
opsi, operf]
-- operators whose second argument is a dummy variable
dummyvarop1 := [opdiff,opalg, opint, opsum, opprod]
-- operators whose second and third arguments are dummy variables
dummyvarop2 := [opdint, opdsum, opdprod]
operator s ==
if (deref brandNew?) then startUp false
for op in allop repeat
is?(op, s) => return copy op
operator(s)$OP
dpi l == '%pi::O
dfact x == postfix("!"::Symbol::O, (not %pair?(x)$Foreign(Builtin) => x; paren x))
dquote l == prefix(quote(first(l)::O), rest l)
dgamma l == prefix(hconcat("|"::Symbol::O, overbar(" "::Symbol::O)), l)
setDummyVar(op, n) == setProperty(op, DUMMYVAR, n pretend None)
dexp x ==
e := '%e::O
x = 1::O => e
e ** x
startUp b ==
setref(brandNew?,b)
display(oppren, paren)
display(opbox, commaSeparate)
display(oppi, dpi)
display(opexp, dexp)
display(opGamma, dgamma)
display(opGamma2, dgamma)
display(opfact, dfact)
display(opquote, dquote)
display(opperm, supersub('A::O, #1))
display(opbinom, binomial(first #1, second #1))
display(oppow, first(#1) ** second(#1))
display(opsum, sum(first #1, second #1, third #1))
display(opprod, prod(first #1, second #1, third #1))
display(opint, int(first #1 * hconcat('d::O, second #1),
empty(), third #1))
input(oppren, convert concat(convert("("::Symbol)@InputForm,
concat(#1, convert(")"::Symbol)@InputForm)))
input(oppow, convert concat(convert("**"::Symbol)@InputForm, #1))
input(oproot,
convert [convert("**"::Symbol)@InputForm, first #1, 1 / second #1])
for op in algop repeat assert(op, ALGOP)
for op in rtrigop repeat assert(op, 'rtrig)
for op in htrigop repeat assert(op, 'htrig)
for op in trigop repeat assert(op, 'trig)
for op in elemop repeat assert(op, 'elem)
for op in primop repeat assert(op, 'prim)
for op in combop repeat assert(op, 'comb)
for op in specop repeat assert(op, 'special)
for op in anyop repeat assert(op, 'any)
for op in evenop repeat assert(op, EVEN)
for op in oddop repeat assert(op, ODD)
for op in dummyvarop1 repeat setDummyVar(op, 1)
for op in dummyvarop2 repeat setDummyVar(op, 2)
assert(oppren, 'linear)
|