CVC3::ArithTheoremProducer3 Class Reference

#include <arith_theorem_producer3.h>

Inheritance diagram for CVC3::ArithTheoremProducer3:

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Collaboration diagram for CVC3::ArithTheoremProducer3:

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List of all members.

Public Member Functions

ArithTheoremProducer3 (TheoremManager *tm, TheoryArith3 *theoryArith)
Constructor.
Expr rat (Rational r)
Create Expr from Rational (for convenience).
Type realType ()
Type intType ()
Expr darkShadow (const Expr &lhs, const Expr &rhs)
Construct the dark shadow expression representing lhs <= rhs.
Expr grayShadow (const Expr &v, const Expr &e, const Rational &c1, const Rational &c2)
Construct the gray shadow expression representing c1 <= v - e <= c2.
virtual Theorem varToMult (const Expr &e)
==> e = 1 * e
virtual Theorem uMinusToMult (const Expr &e)
==> -(e) = (-1) * e
virtual Theorem minusToPlus (const Expr &x, const Expr &y)
==> x - y = x + (-1) * y
virtual Theorem canonUMinusToDivide (const Expr &e)
-(e) ==> e / (-1); takes 'e'
virtual Theorem canonDivideConst (const Expr &c, const Expr &d)
(c) / d ==> (c/d), takes c and d
virtual Theorem canonDivideMult (const Expr &cx, const Expr &d)
(c * x) / d ==> (c/d) * x, takes (c*x) and d
virtual Theorem canonDividePlus (const Expr &e, const Expr &d)
(+ c ...)/d ==> push division to all the coefficients.
virtual Theorem canonDivideVar (const Expr &e1, const Expr &e2)
x / d ==> (1/d) * x, takes x and d
virtual Expr simplifiedMultExpr (std::vector< Expr > &mulKids)
virtual Expr canonMultConstMult (const Expr &c, const Expr &e)
virtual Expr canonMultConstPlus (const Expr &e1, const Expr &e2)
virtual Expr canonMultPowPow (const Expr &e1, const Expr &e2)
virtual Expr canonMultPowLeaf (const Expr &e1, const Expr &e2)
virtual Expr canonMultLeafLeaf (const Expr &e1, const Expr &e2)
virtual Expr canonMultLeafOrPowMult (const Expr &e1, const Expr &e2)
virtual Expr canonCombineLikeTerms (const std::vector< Expr > &sumExprs)
virtual Expr canonMultLeafOrPowOrMultPlus (const Expr &e1, const Expr &e2)
virtual Expr canonMultPlusPlus (const Expr &e1, const Expr &e2)
virtual Theorem canonMultMtermMterm (const Expr &e)
virtual Theorem canonPlus (const Expr &e)
Canonize (PLUS t1 ... tn).
virtual Theorem canonInvertConst (const Expr &e)
virtual Theorem canonInvertLeaf (const Expr &e)
virtual Theorem canonInvertPow (const Expr &e)
virtual Theorem canonInvertMult (const Expr &e)
virtual Theorem canonInvert (const Expr &e)
==> 1/e = e' where e' is canonical; takes e.
virtual Theorem moveSumConstantRight (const Expr &e)
virtual Theorem canonDivide (const Expr &e)
virtual Theorem canonMult (const Expr &e)
virtual Theorem canonMultTermConst (const Expr &c, const Expr &t)
t*c ==> c*t, takes constant c and term t
virtual Theorem canonMultTerm1Term2 (const Expr &t1, const Expr &t2)
t1*t2 ==> Error, takes t1 and t2 where both are non-constants
virtual Theorem canonMultZero (const Expr &e)
0*t ==> 0, takes 0*t
virtual Theorem canonMultOne (const Expr &e)
1*t ==> t, takes 1*t
virtual Theorem canonMultConstConst (const Expr &c1, const Expr &c2)
c1*c2 ==> c', takes constant c1*c2
virtual Theorem canonMultConstTerm (const Expr &c1, const Expr &c2, const Expr &t)
c1*(c2*t) ==> c'*t, takes c1 and c2 and t
virtual Theorem canonMultConstSum (const Expr &c1, const Expr &sum)
c1*(+ c2 v1 ...) ==> (+ c' c1v1 ...), takes c1 and the sum
virtual Theorem canonPowConst (const Expr &pow)
c^n = c' (compute the constant power expression)
virtual Theorem canonFlattenSum (const Expr &e)
flattens the input. accepts a PLUS expr
virtual Theorem canonComboLikeTerms (const Expr &e)
combine like terms. accepts a flattened PLUS expr
virtual Theorem multEqZero (const Expr &expr)
virtual Theorem powEqZero (const Expr &expr)
virtual Theorem elimPower (const Expr &expr)
virtual Theorem elimPowerConst (const Expr &expr, const Rational &root)
virtual Theorem evenPowerEqNegConst (const Expr &expr)
virtual Theorem intEqIrrational (const Expr &expr, const Theorem &isInt)
virtual Theorem constPredicate (const Expr &e)
e0 @ e1 <==> true | false, where @ is {=,<,<=,>,>=}
virtual Theorem rightMinusLeft (const Expr &e)
e[0] @ e[1] <==> 0 @ e[1] - e[0], where @ is {=,<,<=,>,>=}
virtual Theorem leftMinusRight (const Expr &e)
e[0] @ e[1] <==> e[0] - e[1] @ 0, where @ is {=,<,<=,>,>=}
virtual Theorem plusPredicate (const Expr &x, const Expr &y, const Expr &z, int kind)
x @ y <==> x + z @ y + z, where @ is {=,<,<=,>,>=} (given as 'kind')
virtual Theorem multEqn (const Expr &x, const Expr &y, const Expr &z)
x = y <==> x * z = y * z, where z is a non-zero constant
virtual Theorem divideEqnNonConst (const Expr &x, const Expr &y, const Expr &z)
virtual Theorem multIneqn (const Expr &e, const Expr &z)
Multiplying inequation by a non-zero constant.
virtual Theorem eqToIneq (const Expr &e)
x = y ==> x <= y and x >= y
virtual Theorem flipInequality (const Expr &e)
"op1 GE|GT op2" <==> op2 LE|LT op1
Theorem negatedInequality (const Expr &e)
Propagating negation over <,<=,>,>=.
Theorem realShadow (const Theorem &alphaLTt, const Theorem &tLTbeta)
Real shadow: a <(=) t, t <(=) b ==> a <(=) b.
Theorem realShadowEq (const Theorem &alphaLEt, const Theorem &tLEalpha)
alpha <= t <= alpha ==> t = alpha
Theorem finiteInterval (const Theorem &aLEt, const Theorem &tLEac, const Theorem &isInta, const Theorem &isIntt)
Finite interval for integers: a <= t <= a + c ==> G(t, a, 0, c).
Theorem darkGrayShadow2ab (const Theorem &betaLEbx, const Theorem &axLEalpha, const Theorem &isIntAlpha, const Theorem &isIntBeta, const Theorem &isIntx)
Dark & Gray shadows when a <= b.
Theorem darkGrayShadow2ba (const Theorem &betaLEbx, const Theorem &axLEalpha, const Theorem &isIntAlpha, const Theorem &isIntBeta, const Theorem &isIntx)
Dark & Gray shadows when b <= a.
Theorem expandDarkShadow (const Theorem &darkShadow)
Theorem expandGrayShadow0 (const Theorem &grayShadow)
GRAY_SHADOW(v, e, c, c) ==> v=e+c.
Theorem splitGrayShadow (const Theorem &grayShadow)
G(x, e, c1, c2) ==> (G1 or G2) and (!G1 or !G2).
Theorem splitGrayShadowSmall (const Theorem &grayShadow)
Theorem expandGrayShadow (const Theorem &grayShadow)
G(x, e, c1, c2) ==> e+c1 <= x AND x <= e+c2.
Theorem expandGrayShadowConst (const Theorem &grayShadow)
Optimized rules: GRAY_SHADOW(a*x, c, c1, c2) ==> [expansion].
Theorem grayShadowConst (const Theorem &g)
|- G(ax, c, c1, c2) ==> |- G(x, 0, ceil((c1+c)/a), floor((c2+c)/a))
Rational constRHSGrayShadow (const Rational &c, const Rational &b, const Rational &a)
Implements j(c,b,a).
Theorem lessThanToLE (const Theorem &less, const Theorem &isIntLHS, const Theorem &isIntRHS, bool changeRight)
Theorem lessThanToLERewrite (const Expr &ineq, const Theorem &isIntLHS, const Theorem &isIntRHS, bool changeRight)
Theorem intVarEqnConst (const Expr &eqn, const Theorem &isIntx)
Theorem IsIntegerElim (const Theorem &isIntx)
Theorem eqElimIntRule (const Theorem &eqn, const Theorem &isIntx, const std::vector< Theorem > &isIntVars)
Equality elimination rule for integers:
$\frac{\mathsf{int}(a\cdot x)\quad \mathsf{int}(C+\sum_{i=1}^{n}a_{i}\cdot x_{i})} {a\cdot x=C+\sum_{i=1}^{n}a_{i}\cdot x_{i} \quad\equiv\quad x=t_{2}\wedge 0=t_{3}}$
See the detailed description for explanations.
Theorem isIntConst (const Expr &e)
return e <=> TRUE/FALSE for e == IS_INTEGER(c), where c is a constant
Theorem equalLeaves1 (const Theorem &e)
Theorem equalLeaves2 (const Theorem &e)
Theorem equalLeaves3 (const Theorem &e)
Theorem equalLeaves4 (const Theorem &e)
Theorem diseqToIneq (const Theorem &diseq)
x /= y ==> (x < y) OR (x > y)
Theorem dummyTheorem (const Expr &e)
Theorem oneElimination (const Expr &x)
Theorem clashingBounds (const Theorem &lowerBound, const Theorem &upperBound)
Theorem addInequalities (const Theorem &thm1, const Theorem &thm2)
Theorem addInequalities (const std::vector< Theorem > &thms)
Theorem implyWeakerInequality (const Expr &expr1, const Expr &expr2)
Theorem implyNegatedInequality (const Expr &expr1, const Expr &expr2)
Theorem integerSplit (const Expr &intVar, const Rational &intPoint)
Theorem trustedRewrite (const Expr &expr1, const Expr &expr2)
Theorem rafineStrictInteger (const Theorem &isIntConstrThm, const Expr &constr)
Theorem simpleIneqInt (const Expr &ineq, const Theorem &isIntRHS)
Theorem intEqualityRationalConstant (const Theorem &isIntConstrThm, const Expr &constr)
Theorem cycleConflict (const std::vector< Theorem > &inequalitites)
Theorem implyEqualities (const std::vector< Theorem > &inequalities)
Theorem implyWeakerInequalityDiffLogic (const std::vector< Theorem > &antecedentThms, const Expr &implied)
Theorem implyNegatedInequalityDiffLogic (const std::vector< Theorem > &antecedentThms, const Expr &implied)
Theorem expandGrayShadowRewrite (const Expr &theShadow)
Theorem compactNonLinearTerm (const Expr &nonLinear)
Theorem nonLinearIneqSignSplit (const Theorem &ineqThm)
Theorem implyDiffLogicBothBounds (const Expr &x, std::vector< Theorem > &c1_le_x, Rational c1, std::vector< Theorem > &x_le_c2, Rational c2)
Theorem powerOfOne (const Expr &e)

Static Public Member Functions

static bool greaterthan (const Expr &, const Expr &)

Private Member Functions

Auxiliary functions for eqElimIntRule()

Methods that compute the subterms used in eqElimIntRule()

Rational modEq (const Rational &i, const Rational &m)
Compute the special modulus: i - m*floor(i/m+1/2).
Expr create_t (const Expr &eqn)
Create the term 't'. See eqElimIntRule().
Expr create_t2 (const Expr &lhs, const Expr &rhs, const Expr &t)
Create the term 't2'. See eqElimIntRule().
Expr create_t3 (const Expr &lhs, const Expr &rhs, const Expr &t)
Create the term 't3'. See eqElimIntRule().
void sumModM (std::vector< Expr > &summands, const Expr &sum, const Rational &m, const Rational &divisor)
Takes sum = a_0 + a_1*x_1+...+a_n*x_n and returns the vector of similar monomials (in 'summands') with coefficients mod(a_i, m). If divide flag is true, the coefficients will be mod(a_i,m)/m.
Expr monomialModM (const Expr &e, const Rational &m, const Rational &divisor)
Compute the special modulus: i - m*floor(i/m+1/2).
void sumMulF (std::vector< Expr > &summands, const Expr &sum, const Rational &m, const Rational &divisor)
Compute the special modulus: i - m*floor(i/m+1/2).
Expr monomialMulF (const Expr &e, const Rational &m, const Rational &divisor)
Compute the special modulus: i - m*floor(i/m+1/2).
Rational f (const Rational &i, const Rational &m)
Compute floor(i/m+1/2) + mod(i,m).
Expr substitute (const Expr &term, ExprMap< Expr > &eMap)
Compute the special modulus: i - m*floor(i/m+1/2).

Private Attributes

TheoryArith3 * d_theoryArith

Detailed Description

Definition at line 32 of file arith_theorem_producer3.h.

Constructor & Destructor Documentation

CVC3::ArithTheoremProducer3::ArithTheoremProducer3	(	TheoremManager *	tm,
		TheoryArith3 *	theoryArith
	)			`[inline]`

Constructor.

Definition at line 66 of file arith_theorem_producer3.h.

Member Function Documentation

Rational ArithTheoremProducer3::modEq	(	const Rational &	i,
		const Rational &	m
	)			`[private]`

Compute the special modulus: i - m*floor(i/m+1/2).

Definition at line 2227 of file arith_theorem_producer3.cpp.

References DebugAssert, CVC3::Rational::toString(), and CVC3::TRACE.

Referenced by f(), monomialModM(), and sumModM().

Expr ArithTheoremProducer3::create_t ( const Expr & eqn ) [private]

Create the term 't'. See eqElimIntRule().

Definition at line 2167 of file arith_theorem_producer3.cpp.

References CLASS_NAME, DebugAssert, CVC3::Expr::getRational(), CVC3::isMult(), CVC3::isPlus(), monomialModM(), CVC3::multExpr(), CVC3::plusExpr(), rat(), sumModM(), CVC3::Rational::toString(), and CVC3::Expr::toString().

Expr ArithTheoremProducer3::create_t2	(	const Expr &	lhs,
		const Expr &	rhs,
		const Expr &	t
	)			`[private]`

Create the term 't2'. See eqElimIntRule().

Definition at line 2186 of file arith_theorem_producer3.cpp.

References DebugAssert, CVC3::Expr::getRational(), CVC3::isPlus(), CVC3::Expr::isRational(), monomialModM(), CVC3::plusExpr(), rat(), sumModM(), and CVC3::Rational::toString().

Referenced by eqElimIntRule().

Expr ArithTheoremProducer3::create_t3	(	const Expr &	lhs,
		const Expr &	rhs,
		const Expr &	t
	)			`[private]`

Create the term 't3'. See eqElimIntRule().

Definition at line 2206 of file arith_theorem_producer3.cpp.

References DebugAssert, CVC3::Expr::getRational(), CVC3::isPlus(), CVC3::Expr::isRational(), monomialMulF(), CVC3::plusExpr(), rat(), sumMulF(), and CVC3::Rational::toString().

Referenced by eqElimIntRule().

void ArithTheoremProducer3::sumModM	(	std::vector< Expr > &	summands,
		const Expr &	sum,
		const Rational &	m,
		const Rational &	divisor
	)			`[private]`

Takes sum = a_0 + a_1*x_1+...+a_n*x_n and returns the vector of similar monomials (in 'summands') with coefficients mod(a_i, m). If divide flag is true, the coefficients will be mod(a_i,m)/m.

Definition at line 2243 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), CLASS_NAME, DebugAssert, CVC3::Expr::end(), CVC3::Expr::getRational(), CVC3::Expr::isRational(), modEq(), monomialModM(), rat(), and CVC3::Rational::toString().

Referenced by create_t(), and create_t2().

Expr ArithTheoremProducer3::monomialModM	(	const Expr &	e,
		const Rational &	m,
		const Rational &	divisor
	)			`[private]`

Compute the special modulus: i - m*floor(i/m+1/2).

Definition at line 2263 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), DebugAssert, CVC3::Expr::getKids(), CVC3::Expr::getRational(), CVC3::isMult(), modEq(), CVC3::multExpr(), rat(), CVC3::Expr::toString(), CVC3::Rational::toString(), and CVC3::TRACE.

Referenced by create_t(), create_t2(), and sumModM().

void ArithTheoremProducer3::sumMulF	(	std::vector< Expr > &	summands,
		const Expr &	sum,
		const Rational &	m,
		const Rational &	divisor
	)			`[private]`

Compute the special modulus: i - m*floor(i/m+1/2).

Definition at line 2291 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), CLASS_NAME, DebugAssert, CVC3::Expr::end(), f(), CVC3::Expr::getRational(), CVC3::Expr::isRational(), monomialMulF(), rat(), and CVC3::Rational::toString().

Referenced by create_t3().

Expr ArithTheoremProducer3::monomialMulF	(	const Expr &	e,
		const Rational &	m,
		const Rational &	divisor
	)			`[private]`

Compute the special modulus: i - m*floor(i/m+1/2).

Definition at line 2311 of file arith_theorem_producer3.cpp.

References DebugAssert, f(), CVC3::isMult(), CVC3::multExpr(), rat(), and CVC3::Rational::toString().

Referenced by create_t3(), and sumMulF().

Rational ArithTheoremProducer3::f	(	const Rational &	i,
		const Rational &	m
	)			`[private]`

Compute floor(i/m+1/2) + mod(i,m).

Definition at line 2236 of file arith_theorem_producer3.cpp.

References DebugAssert, modEq(), and CVC3::Rational::toString().

Referenced by monomialMulF(), and sumMulF().

Expr ArithTheoremProducer3::substitute	(	const Expr &	term,
		ExprMap< Expr > &	eMap
	)			`[private]`

Compute the special modulus: i - m*floor(i/m+1/2).

Definition at line 2328 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), CVC3::Expr::end(), CVC3::ExprMap< Data >::end(), CVC3::ExprMap< Data >::find(), CVC3::isMult(), CVC3::isPlus(), and CVC3::plusExpr().

Expr CVC3::ArithTheoremProducer3::rat ( Rational r ) [inline]

Create Expr from Rational (for convenience).

Definition at line 70 of file arith_theorem_producer3.h.

References CVC3::TheoremProducer::d_em, and CVC3::ExprManager::newRatExpr().

Referenced by canonCombineLikeTerms(), canonComboLikeTerms(), canonDivideConst(), canonDivideMult(), canonDividePlus(), canonDivideVar(), canonInvertConst(), canonInvertLeaf(), canonInvertMult(), canonInvertPow(), canonMultConstConst(), canonMultConstMult(), canonMultConstTerm(), canonMultLeafLeaf(), canonMultLeafOrPowMult(), canonMultOne(), canonMultPowLeaf(), canonMultPowPow(), canonMultZero(), canonPowConst(), canonUMinusToDivide(), create_t(), create_t2(), create_t3(), darkGrayShadow2ab(), darkGrayShadow2ba(), divideEqnNonConst(), elimPowerConst(), eqElimIntRule(), expandGrayShadow(), expandGrayShadowConst(), grayShadowConst(), integerSplit(), intVarEqnConst(), leftMinusRight(), lessThanToLE(), lessThanToLERewrite(), minusToPlus(), monomialModM(), monomialMulF(), moveSumConstantRight(), multEqZero(), powEqZero(), rafineStrictInteger(), rightMinusLeft(), simplifiedMultExpr(), sumModM(), sumMulF(), uMinusToMult(), and varToMult().

Type CVC3::ArithTheoremProducer3::realType ( ) [inline]

Definition at line 71 of file arith_theorem_producer3.h.

References d_theoryArith, and CVC3::TheoryArith::realType().

Type CVC3::ArithTheoremProducer3::intType ( ) [inline]

Definition at line 72 of file arith_theorem_producer3.h.

References d_theoryArith, and CVC3::TheoryArith::intType().

Referenced by eqElimIntRule().

Expr CVC3::ArithTheoremProducer3::darkShadow	(	const Expr &	lhs,
		const Expr &	rhs
	)			`[inline]`

Construct the dark shadow expression representing lhs <= rhs.

Definition at line 74 of file arith_theorem_producer3.h.

References d_theoryArith, and CVC3::TheoryArith::darkShadow().

Referenced by darkGrayShadow2ab(), and darkGrayShadow2ba().

Expr CVC3::ArithTheoremProducer3::grayShadow	(	const Expr &	v,
		const Expr &	e,
		const Rational &	c1,
		const Rational &	c2
	)			`[inline]`

Construct the gray shadow expression representing c1 <= v - e <= c2.

Alternatively, v = e + i for some i s.t. c1 <= i <= c2

Definition at line 80 of file arith_theorem_producer3.h.

References d_theoryArith, and CVC3::TheoryArith::grayShadow().

Referenced by darkGrayShadow2ab(), darkGrayShadow2ba(), finiteInterval(), grayShadowConst(), and splitGrayShadow().

Theorem ArithTheoremProducer3::varToMult ( const Expr & e ) [virtual]

==> e = 1 * e

Implements CVC3::ArithProofRules.

Definition at line 56 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::uMinusToMult ( const Expr & e ) [virtual]

==> -(e) = (-1) * e

Implements CVC3::ArithProofRules.

Definition at line 64 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::minusToPlus	(	const Expr &	x,
		const Expr &	y
	)			`[virtual]`

==> x - y = x + (-1) * y

Implements CVC3::ArithProofRules.

Definition at line 72 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonUMinusToDivide ( const Expr & e ) [virtual]

-(e) ==> e / (-1); takes 'e'

Canon Rule for unary minus: it just converts it to division by -1, the result is not yet canonical:

Implements CVC3::ArithProofRules.

Definition at line 82 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonDivideConst	(	const Expr &	c,
		const Expr &	d
	)			`[virtual]`

(c) / d ==> (c/d), takes c and d

Canon Rules for division by constant 'd'

Implements CVC3::ArithProofRules.

Definition at line 91 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::TheoremProducer::d_hole, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonDivideMult	(	const Expr &	cx,
		const Expr &	d
	)			`[virtual]`

(c * x) / d ==> (c/d) * x, takes (c*x) and d

Implements CVC3::ArithProofRules.

Definition at line 110 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::isMult(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonDividePlus	(	const Expr &	e,
		const Expr &	d
	)			`[virtual]`

(+ c ...)/d ==> push division to all the coefficients.

The result is not canonical, but canonizing the summands will make it canonical. Takes (+ c ...) and d

Implements CVC3::ArithProofRules.

Definition at line 138 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::isPlus(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::plusExpr(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonDivideVar	(	const Expr &	e,
		const Expr &	d
	)			`[virtual]`

x / d ==> (1/d) * x, takes x and d

Implements CVC3::ArithProofRules.

Definition at line 161 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

bool ArithTheoremProducer3::greaterthan	(	const Expr &	l,
		const Expr &	r
	)			`[static]`

Definition at line 2354 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), DebugAssert, CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::Expr::isRational(), CVC3::MULT, CVC3::PLUS, CVC3::POW, and CVC3::RATIONAL_EXPR.

Referenced by MonomialLess::operator()().

Expr ArithTheoremProducer3::simplifiedMultExpr ( std::vector< Expr > & mulKids ) [virtual]

Definition at line 196 of file arith_theorem_producer3.cpp.

References DebugAssert, CVC3::multExpr(), and rat().

Referenced by canonMultConstMult(), canonMultLeafLeaf(), canonMultLeafOrPowMult(), canonMultPowLeaf(), and canonMultPowPow().

Expr ArithTheoremProducer3::canonMultConstMult	(	const Expr &	c,
		const Expr &	e
	)			`[virtual]`

Definition at line 209 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), DebugAssert, CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::isRational(), CVC3::Expr::isRational(), CVC3::MULT, rat(), simplifiedMultExpr(), and CVC3::Expr::toString().

Referenced by canonMultMtermMterm().

Expr ArithTheoremProducer3::canonMultConstPlus	(	const Expr &	e1,
		const Expr &	e2
	)			`[virtual]`

Definition at line 231 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), canonMultMtermMterm(), d_theoryArith, DebugAssert, CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::Expr::getOp(), CVC3::Theorem::getRHS(), CVC3::Expr::isRational(), CVC3::PLUS, and CVC3::Theory::substitutivityRule().

Referenced by canonMultMtermMterm().

Expr ArithTheoremProducer3::canonMultPowPow	(	const Expr &	e1,
		const Expr &	e2
	)			`[virtual]`

Definition at line 250 of file arith_theorem_producer3.cpp.

References DebugAssert, CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::POW, CVC3::powExpr(), rat(), and simplifiedMultExpr().

Referenced by canonMultMtermMterm().

Expr ArithTheoremProducer3::canonMultPowLeaf	(	const Expr &	e1,
		const Expr &	e2
	)			`[virtual]`

Definition at line 290 of file arith_theorem_producer3.cpp.

References DebugAssert, CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::POW, CVC3::powExpr(), rat(), and simplifiedMultExpr().

Referenced by canonMultMtermMterm().

Expr ArithTheoremProducer3::canonMultLeafLeaf	(	const Expr &	e1,
		const Expr &	e2
	)			`[virtual]`

Definition at line 329 of file arith_theorem_producer3.cpp.

References CVC3::powExpr(), rat(), and simplifiedMultExpr().

Referenced by canonMultMtermMterm().

Expr ArithTheoremProducer3::canonMultLeafOrPowMult	(	const Expr &	e1,
		const Expr &	e2
	)			`[virtual]`

Definition at line 357 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), DebugAssert, CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::MULT, CVC3::POW, CVC3::powExpr(), rat(), and simplifiedMultExpr().

Referenced by canonMultMtermMterm().

Expr ArithTheoremProducer3::canonCombineLikeTerms ( const std::vector< Expr > & sumExprs ) [virtual]

Definition at line 429 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), canonMultMtermMterm(), DebugAssert, CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::Theorem::getRHS(), CVC3::Expr::isRational(), CVC3::MULT, CVC3::multExpr(), CVC3::plusExpr(), and rat().

Referenced by canonMultLeafOrPowOrMultPlus(), canonMultPlusPlus(), and canonPlus().

Expr ArithTheoremProducer3::canonMultLeafOrPowOrMultPlus	(	const Expr &	e1,
		const Expr &	e2
	)			`[virtual]`

Definition at line 510 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), canonCombineLikeTerms(), canonMultMtermMterm(), DebugAssert, CVC3::Expr::end(), CVC3::Expr::getKind(), and CVC3::PLUS.

Referenced by canonMultMtermMterm().

Expr ArithTheoremProducer3::canonMultPlusPlus	(	const Expr &	e1,
		const Expr &	e2
	)			`[virtual]`

Definition at line 529 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), canonCombineLikeTerms(), canonMultMtermMterm(), DebugAssert, CVC3::Expr::end(), CVC3::Expr::getKind(), and CVC3::PLUS.

Referenced by canonMultMtermMterm().

Theorem ArithTheoremProducer3::canonMultMtermMterm ( const Expr & e ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 553 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), canonMultConstConst(), canonMultConstMult(), canonMultConstPlus(), canonMultLeafLeaf(), canonMultLeafOrPowMult(), canonMultLeafOrPowOrMultPlus(), canonMultOne(), canonMultPlusPlus(), canonMultPowLeaf(), canonMultPowPow(), canonMultZero(), CHECK_PROOFS, CHECK_SOUND, d_theoryArith, CVC3::Assumptions::emptyAssump(), FatalAssert, CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::Theorem::getRHS(), CVC3::isMult(), CVC3::Expr::isRational(), CVC3::MULT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::PLUS, CVC3::POW, CVC3::RATIONAL_EXPR, CVC3::Theory::reflexivityRule(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Referenced by canonCombineLikeTerms(), canonInvertMult(), canonMult(), canonMultConstPlus(), canonMultLeafOrPowOrMultPlus(), and canonMultPlusPlus().

Theorem ArithTheoremProducer3::canonPlus ( const Expr & e ) [virtual]

Canonize (PLUS t1 ... tn).

Implements CVC3::ArithProofRules.

Definition at line 718 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), canonCombineLikeTerms(), DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::PLUS, and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonInvertConst ( const Expr & e ) [virtual]

Definition at line 769 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Referenced by canonInvert().

Theorem ArithTheoremProducer3::canonInvertLeaf ( const Expr & e ) [virtual]

Definition at line 785 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::powExpr(), rat(), and CVC3::TheoremProducer::withProof().

Referenced by canonInvert().

Theorem ArithTheoremProducer3::canonInvertPow ( const Expr & e ) [virtual]

Definition at line 797 of file arith_theorem_producer3.cpp.

References DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getKind(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::POW, CVC3::powExpr(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Referenced by canonInvert().

Theorem ArithTheoremProducer3::canonInvertMult ( const Expr & e ) [virtual]

Definition at line 816 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), canonInvert(), canonMultMtermMterm(), DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getKind(), CVC3::Theorem::getRHS(), CVC3::MULT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Referenced by canonInvert().

Theorem ArithTheoremProducer3::canonInvert ( const Expr & e ) [virtual]

==> 1/e = e' where e' is canonical; takes e.

Implements CVC3::ArithProofRules.

Definition at line 839 of file arith_theorem_producer3.cpp.

References canonInvertConst(), canonInvertLeaf(), canonInvertMult(), canonInvertPow(), DebugAssert, CVC3::Expr::getKind(), CVC3::MULT, CVC3::PLUS, CVC3::POW, CVC3::RATIONAL_EXPR, and CVC3::Expr::toString().

Referenced by canonDivide(), and canonInvertMult().

Theorem ArithTheoremProducer3::moveSumConstantRight ( const Expr & e ) [virtual]

Transform e = (SUM r t1 ... tn) @ 0 into (SUM t1 ... tn) @ -r. The first sum term (r) must be a rational and t1 ... tn terms must be canonised.

Parameters:

e

the expression to transform

Returns:: rewrite theorem representing the transformation

Implements CVC3::ArithProofRules.

Definition at line 861 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::Expr::isEq(), CVC3::isIneq(), CVC3::isPlus(), CVC3::Expr::isRational(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::plusExpr(), rat(), MiniSat::right(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonDivide ( const Expr & e ) [virtual]

e[0]/e[1] ==> e[0]*(e[1])^-1

Implements CVC3::ArithProofRules.

Definition at line 907 of file arith_theorem_producer3.cpp.

References canonInvert(), canonMult(), d_theoryArith, DebugAssert, CVC3::DIVIDE, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getKind(), CVC3::Theorem::getRHS(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), CVC3::Theory::transitivityRule(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonMult ( const Expr & e ) [virtual]

Multiply out the operands of the multiplication (each of them is expected to be canonised

Implements CVC3::ArithProofRules.

Definition at line 751 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), canonMultMtermMterm(), DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::Theorem::getRHS(), CVC3::MULT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), and CVC3::TheoremProducer::withProof().

Referenced by canonDivide().

Theorem ArithTheoremProducer3::canonMultTermConst	(	const Expr &	c,
		const Expr &	t
	)			`[virtual]`

t*c ==> c*t, takes constant c and term t

Implements CVC3::ArithProofRules.

Definition at line 925 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::Assumptions::emptyAssump(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonMultTerm1Term2	(	const Expr &	t1,
		const Expr &	t2
	)			`[virtual]`

t1*t2 ==> Error, takes t1 and t2 where both are non-constants

Implements CVC3::ArithProofRules.

Definition at line 939 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, and CVC3::Expr::toString().

Theorem ArithTheoremProducer3::canonMultZero ( const Expr & e ) [virtual]

0*t ==> 0, takes 0*t

Implements CVC3::ArithProofRules.

Definition at line 952 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), and CVC3::TheoremProducer::withProof().

Referenced by canonMultMtermMterm().

Theorem ArithTheoremProducer3::canonMultOne ( const Expr & e ) [virtual]

1*t ==> t, takes 1*t

Implements CVC3::ArithProofRules.

Definition at line 960 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), and CVC3::TheoremProducer::withProof().

Referenced by canonMultMtermMterm().

Theorem ArithTheoremProducer3::canonMultConstConst	(	const Expr &	c1,
		const Expr &	c2
	)			`[virtual]`

c1*c2 ==> c', takes constant c1*c2

Implements CVC3::ArithProofRules.

Definition at line 969 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Referenced by canonMultMtermMterm().

Theorem ArithTheoremProducer3::canonMultConstTerm	(	const Expr &	c1,
		const Expr &	c2,
		const Expr &	t
	)			`[virtual]`

c1*(c2*t) ==> c'*t, takes c1 and c2 and t

Implements CVC3::ArithProofRules.

Definition at line 987 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonMultConstSum	(	const Expr &	c1,
		const Expr &	sum
	)			`[virtual]`

c1*(+ c2 v1 ...) ==> (+ c' c1v1 ...), takes c1 and the sum

Implements CVC3::ArithProofRules.

Definition at line 1007 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::PLUS, CVC3::plusExpr(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonPowConst ( const Expr & pow ) [virtual]

c^n = c' (compute the constant power expression)

Implements CVC3::ArithProofRules.

Definition at line 1030 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::Rational::isInteger(), CVC3::Expr::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::pow(), CVC3::POW, rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonFlattenSum ( const Expr & e ) [virtual]

flattens the input. accepts a PLUS expr

Implements CVC3::ArithProofRules.

Definition at line 1057 of file arith_theorem_producer3.cpp.

References CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::getKind(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::PLUS, CVC3::plusExpr(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::canonComboLikeTerms ( const Expr & e ) [virtual]

combine like terms. accepts a flattened PLUS expr

Implements CVC3::ArithProofRules.

Definition at line 1084 of file arith_theorem_producer3.cpp.

References CVC3::ExprMap< Data >::begin(), CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::ExprMap< Data >::count(), CVC3::Assumptions::emptyAssump(), CVC3::ExprMap< Data >::end(), CVC3::Expr::end(), CVC3::isMult(), CVC3::isPlus(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::plusExpr(), rat(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::multEqZero ( const Expr & expr ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 1142 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::getRational(), CVC3::Expr::isEq(), CVC3::isMult(), CVC3::Expr::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::OR, rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::powEqZero ( const Expr & expr ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 1165 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::ExprManager::falseExpr(), CVC3::Expr::getRational(), CVC3::Expr::isEq(), CVC3::isPow(), CVC3::Expr::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::elimPower ( const Expr & expr ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 1192 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::Expr::getRational(), CVC3::Expr::isEq(), CVC3::isIntegerConst(), CVC3::isPow(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::orExpr(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::elimPowerConst	(	const Expr &	expr,
		const Rational &	root
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 1217 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::Expr::getRational(), CVC3::Expr::isEq(), CVC3::isIntegerConst(), CVC3::isPow(), CVC3::Expr::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::orExpr(), CVC3::pow(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::evenPowerEqNegConst ( const Expr & expr ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 1241 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::ExprManager::falseExpr(), CVC3::Expr::getRational(), CVC3::Expr::isEq(), CVC3::isIntegerConst(), CVC3::isPow(), CVC3::Expr::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::intEqIrrational	(	const Expr &	expr,
		const Theorem &	isInt
	)			`[virtual]`

Theorem ArithTheoremProducer3::constPredicate ( const Expr & e ) [virtual]

e0 @ e1 <==> true | false, where @ is {=,<,<=,>,>=}

Parameters:

e

takes e is (e0@e1) where e0 and e1 are constants

Implements CVC3::ArithProofRules.

Definition at line 1287 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CLASS_NAME, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::EQ, CVC3::ExprManager::falseExpr(), CVC3::GE, CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::GT, CVC3::isRational(), CVC3::LE, CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), CVC3::ExprManager::trueExpr(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::rightMinusLeft ( const Expr & e ) [virtual]

e[0] @ e[1] <==> 0 @ e[1] - e[0], where @ is {=,<,<=,>,>=}

Implements CVC3::ArithProofRules.

Definition at line 1326 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::EQ, CVC3::GE, CVC3::Expr::getKind(), CVC3::Expr::getOp(), CVC3::GT, CVC3::LE, CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::leftMinusRight ( const Expr & e ) [virtual]

e[0] @ e[1] <==> e[0] - e[1] @ 0, where @ is {=,<,<=,>,>=}

Implements CVC3::ArithProofRules.

Definition at line 1344 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::EQ, CVC3::GE, CVC3::Expr::getKind(), CVC3::Expr::getOp(), CVC3::GT, CVC3::LE, CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::plusPredicate	(	const Expr &	x,
		const Expr &	y,
		const Expr &	z,
		int	kind
	)			`[virtual]`

x @ y <==> x + z @ y + z, where @ is {=,<,<=,>,>=} (given as 'kind')

Implements CVC3::ArithProofRules.

Definition at line 1362 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::EQ, CVC3::GE, CVC3::GT, CVC3::LE, MiniSat::left(), CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), MiniSat::right(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::multEqn	(	const Expr &	x,
		const Expr &	y,
		const Expr &	z
	)			`[virtual]`

x = y <==> x * z = y * z, where z is a non-zero constant

Implements CVC3::ArithProofRules.

Definition at line 1381 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::Expr::getRational(), CVC3::Expr::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::divideEqnNonConst	(	const Expr &	x,
		const Expr &	y,
		const Expr &	z
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 1394 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::orExpr(), rat(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::multIneqn	(	const Expr &	e,
		const Expr &	z
	)			`[virtual]`

Multiplying inequation by a non-zero constant.

z>0 ==> e[0] @ e[1] <==> e[0]*z @ e[1]*z

z<0 ==> e[0] @ e[1] <==> e[1]*z @ e[0]*z

for @ in {<,<=,>,>=}:

Implements CVC3::ArithProofRules.

Definition at line 1406 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::GE, CVC3::Expr::getKind(), CVC3::Expr::getOp(), CVC3::Expr::getRational(), CVC3::GT, CVC3::Expr::isRational(), CVC3::LE, CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::eqToIneq ( const Expr & e ) [virtual]

x = y ==> x <= y and x >= y

Implements CVC3::ArithProofRules.

Definition at line 1433 of file arith_theorem_producer3.cpp.

References CVC3::andExpr(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::geExpr(), CVC3::Expr::isEq(), CVC3::leExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::flipInequality ( const Expr & e ) [virtual]

"op1 GE|GT op2" <==> op2 LE|LT op1

Implements CVC3::ArithProofRules.

Definition at line 1455 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::isGE(), CVC3::isGT(), CVC3::LE, CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::negatedInequality ( const Expr & e ) [virtual]

Propagating negation over <,<=,>,>=.

NOT (op1 < op2) <==> (op1 >= op2)

NOT (op1 <= op2) <==> (op1 > op2)

NOT (op1 > op2) <==> (op1 <= op2)

NOT (op1 >= op2) <==> (op1 < op2)

Implements CVC3::ArithProofRules.

Definition at line 1475 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::GE, CVC3::GT, CVC3::isGT(), CVC3::isIneq(), CVC3::isLE(), CVC3::isLT(), CVC3::Expr::isNot(), CVC3::LE, CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::realShadow	(	const Theorem &	alphaLTt,
		const Theorem &	tLTbeta
	)			`[virtual]`

Real shadow: a <(=) t, t <(=) b ==> a <(=) b.

Implements CVC3::ArithProofRules.

Definition at line 1504 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Expr::getKind(), CVC3::Theorem::getProof(), CVC3::isLE(), CVC3::isLT(), CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::realShadowEq	(	const Theorem &	alphaLEt,
		const Theorem &	tLEalpha
	)			`[virtual]`

alpha <= t <= alpha ==> t = alpha

takes two ineqs "|- alpha LE t" and "|- t LE alpha" and returns "|- t = alpha"

Implements CVC3::ArithProofRules.

Definition at line 1539 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::isLE(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::finiteInterval	(	const Theorem &	aLEt,
		const Theorem &	tLEac,
		const Theorem &	isInta,
		const Theorem &	isIntt
	)			`[virtual]`

Finite interval for integers: a <= t <= a + c ==> G(t, a, 0, c).

Implements CVC3::ArithProofRules.

Definition at line 1571 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), grayShadow(), CVC3::isIntPred(), CVC3::isLE(), CVC3::isPlus(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::darkGrayShadow2ab	(	const Theorem &	betaLEbx,
		const Theorem &	axLEalpha,
		const Theorem &	isIntAlpha,
		const Theorem &	isIntBeta,
		const Theorem &	isIntx
	)			`[virtual]`

Dark & Gray shadows when a <= b.

takes two integer ineqs (i.e. all vars are ints) "|- beta <= b.x" and "|- a.x <= alpha" and checks if "1 <= a <= b" and returns (D or G) and (!D or !G), where D = Dark_Shadow(ab-1, b.alpha - a.beta), G = Gray_Shadow(a.x, alpha, -(a-1), 0).

Implements CVC3::ArithProofRules.

Definition at line 1635 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, darkShadow(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::getRational(), grayShadow(), CVC3::isIntPred(), CVC3::isLE(), CVC3::isMult(), CVC3::minusExpr(), CVC3::multExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), rat(), CVC3::Expr::toString(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::darkGrayShadow2ba	(	const Theorem &	betaLEbx,
		const Theorem &	axLEalpha,
		const Theorem &	isIntAlpha,
		const Theorem &	isIntBeta,
		const Theorem &	isIntx
	)			`[virtual]`

Dark & Gray shadows when b <= a.

takes two integer ineqs (i.e. all vars are ints) "|- beta <= b.x" and "|- a.x <= alpha" and checks if "1 <= b < a" and returns (D or G) and (!D or !G), where D = Dark_Shadow(ab-1, b.alpha - a.beta), G = Gray_Shadow(b.x, beta, 0, b-1).

Implements CVC3::ArithProofRules.

Definition at line 1726 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, darkShadow(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::getRational(), grayShadow(), CVC3::isIntPred(), CVC3::isLE(), CVC3::isMult(), CVC3::minusExpr(), CVC3::multExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), rat(), CVC3::Expr::toString(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::expandDarkShadow ( const Theorem & darkShadow ) [virtual]

takes a dark shadow and expands it into an inequality.

Implements CVC3::ArithProofRules.

Definition at line 1811 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::isDarkShadow(), CVC3::leExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::expandGrayShadow0 ( const Theorem & g ) [virtual]

GRAY_SHADOW(v, e, c, c) ==> v=e+c.

Implements CVC3::ArithProofRules.

Definition at line 1826 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::isGrayShadow(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::splitGrayShadow ( const Theorem & g ) [virtual]

G(x, e, c1, c2) ==> (G1 or G2) and (!G1 or !G2).

Here G1 = G(x,e,c1,c), G2 = G(x,e,c+1,c2), and c = floor((c1+c2)/2).

Implements CVC3::ArithProofRules.

Definition at line 1852 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::getRational(), grayShadow(), CVC3::isGrayShadow(), CVC3::Rational::isInteger(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::splitGrayShadowSmall ( const Theorem & grayShadow ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 3024 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::expandGrayShadow ( const Theorem & g ) [virtual]

G(x, e, c1, c2) ==> e+c1 <= x AND x <= e+c2.

Implements CVC3::ArithProofRules.

Definition at line 1889 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::getRational(), CVC3::isGrayShadow(), CVC3::Rational::isInteger(), CVC3::leExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::expandGrayShadowConst ( const Theorem & g ) [virtual]

Optimized rules: GRAY_SHADOW(a*x, c, c1, c2) ==> [expansion].

Implements three versions of the rule:

$\frac{\mathrm{GRAY\_SHADOW}(ax,c,c1,c2)} {ax = c + i - \mathrm{sign}(i)\cdot j(c,i,a) \lor GRAY\_SHADOW(ax, c, i-\mathrm{sign}(i)\cdot (a+j(c,i,a)))}$

where the conclusion may become FALSE or without the GRAY_SHADOW part, depending on the values of a, c and i.

Implements CVC3::ArithProofRules.

Definition at line 1920 of file arith_theorem_producer3.cpp.

References CVC3::abs(), CHECK_PROOFS, CHECK_SOUND, constRHSGrayShadow(), CVC3::TheoremProducer::d_em, CVC3::Expr::eqExpr(), CVC3::ExprManager::falseExpr(), CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::getRational(), CVC3::GRAY_SHADOW, CVC3::isGrayShadow(), CVC3::Rational::isInteger(), CVC3::isMult(), CVC3::Expr::isRational(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::orExpr(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::grayShadowConst ( const Theorem & g ) [virtual]

|- G(ax, c, c1, c2) ==> |- G(x, 0, ceil((c1+c)/a), floor((c2+c)/a))

In the case the new c1 > c2, return |- FALSE

Implements CVC3::ArithProofRules.

Definition at line 1985 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, d_theoryArith, CVC3::ExprManager::falseExpr(), CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::getRational(), grayShadow(), CVC3::isGrayShadow(), CVC3::Rational::isInteger(), CVC3::Expr::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), rat(), CVC3::TheoryArith3::separateMonomial(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Rational ArithTheoremProducer3::constRHSGrayShadow	(	const Rational &	c,
		const Rational &	b,
		const Rational &	a
	)

Implements j(c,b,a).

accepts 3 integers a,b,c and returns (b > 0)? (c+b) mod a : (a - (c+b)) mod a

Definition at line 2025 of file arith_theorem_producer3.cpp.

References DebugAssert, and CVC3::Rational::isInteger().

Referenced by expandGrayShadowConst().

Theorem ArithTheoremProducer3::lessThanToLE	(	const Theorem &	less,
		const Theorem &	isIntLHS,
		const Theorem &	isIntRHS,
		bool	changeRight
	)			`[virtual]`

Takes a Theorem(\alpha < \beta) and returns Theorem(\alpha < \beta <==> \alpha <= \beta -1) where \alpha and \beta are integer expressions

Implements CVC3::ArithProofRules.

Definition at line 2043 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::isIntPred(), CVC3::isLT(), CVC3::leExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::lessThanToLERewrite	(	const Expr &	ineq,
		const Theorem &	isIntLHS,
		const Theorem &	isIntRHS,
		bool	changeRight
	)			`[virtual]`

Takes a Theorem(\alpha < \beta) and returns Theorem(\alpha < \beta <==> \alpha <= \beta -1) where \alpha and \beta are integer expressions

Implements CVC3::ArithProofRules.

Definition at line 3103 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::isIntPred(), CVC3::isLT(), CVC3::leExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::intVarEqnConst	(	const Expr &	eqn,
		const Theorem &	isIntx
	)			`[virtual]`

Parameters:

	eqn	is an equation 0 = a.x or 0 = c + a.x
	isIntx	is a proof of IS_INTEGER(x)

Returns:: the theorem 0 = c + a.x <==> x=-c/a if -c/a is int else return the theorem 0 = c + a.x <==> false.

It also handles the special case of 0 = a.x <==> x = 0

Implements CVC3::ArithProofRules.

Definition at line 2095 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, d_theoryArith, CVC3::Expr::eqExpr(), CVC3::ExprManager::falseExpr(), CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::getRational(), CVC3::Rational::isInteger(), CVC3::isIntPred(), CVC3::isMult(), CVC3::isPlus(), CVC3::Expr::isRational(), CVC3::isRational(), MiniSat::left(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), rat(), MiniSat::right(), CVC3::TheoryArith3::separateMonomial(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::IsIntegerElim ( const Theorem & isIntx ) [virtual]

IS_INTEGER(x) |= EXISTS (y : INT) y = x where x is not already known to be an integer.

Implements CVC3::ArithProofRules.

Definition at line 2480 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, d_theoryArith, DebugAssert, CVC3::Expr::eqExpr(), CVC3::EXISTS, CVC3::Theorem::getExpr(), CVC3::Expr::getKind(), CVC3::Theorem::getProof(), CVC3::TheoryArith::intType(), CVC3::IS_INTEGER, CVC3::TheoryArith3::isInteger(), CVC3::ExprManager::newBoundVarExpr(), CVC3::ExprManager::newClosureExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::eqElimIntRule	(	const Theorem &	eqn,
		const Theorem &	isIntx,
		const std::vector< Theorem > &	isIntVars
	)			`[virtual]`

Equality elimination rule for integers:

$\frac{\mathsf{int}(a\cdot x)\quad \mathsf{int}(C+\sum_{i=1}^{n}a_{i}\cdot x_{i})} {a\cdot x=C+\sum_{i=1}^{n}a_{i}\cdot x_{i} \quad\equiv\quad x=t_{2}\wedge 0=t_{3}}$

See the detailed description for explanations.

This rule implements a step in the iterative algorithm for eliminating integer equality. The terms in the rule are defined as follows:

$\begin{array}{rcl} t_{2} & = & -(C\ \mathbf{mod}\ m+\sum_{i=1}^{n}(a_{i}\ \mathbf{mod}\ m) \cdot x_{i}-m\cdot\sigma(t))\\ & & \\ t_{3} & = & \mathbf{f}(C,m)+\sum_{i=1}^{n}\mathbf{f}(a_{i},m)\cdot x_{i} -a\cdot\sigma(t)\\ & & \\ t & = & (C\ \mathbf{mod}\ m+\sum_{i=1}^{n}(a_{i}\ \mathbf{mod}\ m) \cdot x_{i}+x)/m\\ & & \\ m & = & a+1\\ & & \\ \mathbf{f}(i,m) & = & \left\lfloor \frac{i}{m} +\frac{1}{2}\right\rfloor +i\ \mathbf{mod}\ m\\ & & \\ i\ \mathbf{mod}\ m & = & i-m\left\lfloor\frac{i}{m} +\frac{1}{2}\right\rfloor \end{array}$

All the variables and coefficients are integer, and a >= 2.

Parameters:

eqn

is the equation

$a\cdot x = C + \sum_{i=1}^n a_i\cdot x_i.$

$\frac{\Gamma\models ax=t\quad \Gamma'\models\mathsf{int}(x)\quad \{\Gamma_i\models\mathsf{int}(x_i) | x_i\mbox{ is var in }t\}} {\Gamma,\Gamma',\bigcup_i\Gamma_i\models \exists (y:\mathrm{int}).\ x=t_2(y)\wedge 0=t_3(y)}$

See detailed docs for more information. This rule implements a step in the iterative algorithm for eliminating integer equality. The terms in the rule are defined as follows:

$\begin{array}{rcl} t & = & C+\sum_{i=1}^na_{i}\cdot x_{i}\\ t_{2}(y) & = & -(C\ \mathbf{mod}\ m+\sum_{i=1}^{n}(a_{i}\ \mathbf{mod}\ m) \cdot x_{i}-m\cdot y)\\ & & \\ t_{3}(y) & = & \mathbf{f}(C,m)+\sum_{i=1}^{n}\mathbf{f}(a_{i},m)\cdot x_{i} -a\cdot y\\ & & \\ m & = & a+1\\ & & \\ \mathbf{f}(i,m) & = & \left\lfloor \frac{i}{m} +\frac{1}{2}\right\rfloor +i\ \mathbf{mod}\ m\\ & & \\ i\ \mathbf{mod}\ m & = & i-m\left\lfloor\frac{i}{m} +\frac{1}{2}\right\rfloor \end{array}$

All the variables and coefficients are integer, and a >= 2.

Parameters:

eqn

is the equation ax=t:

$a\cdot x = C + \sum_{i=1}^n a_i\cdot x_i.$

isIntx

is a Theorem deriving the integrality of the LHS variable: IS_INTEGER(x)

isIntVars

is a vector of Theorems deriving the integrality of all variables on the RHS

Implements CVC3::ArithProofRules.

Definition at line 2506 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, create_t2(), create_t3(), CVC3::TheoremProducer::d_em, d_theoryArith, CVC3::Expr::eqExpr(), CVC3::EXISTS, CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Expr::getRational(), CVC3::Theorem::getRHS(), CVC3::int2string(), intType(), CVC3::isDivide(), CVC3::isInt(), CVC3::Rational::isInteger(), CVC3::isIntPred(), CVC3::isPlus(), CVC3::isRational(), CVC3::Theorem::isRewrite(), CVC3::ExprManager::newBoundVarExpr(), CVC3::ExprManager::newClosureExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), rat(), CVC3::TheoryArith3::separateMonomial(), CVC3::Expr::setType(), CVC3::Rational::toString(), CVC3::Expr::toString(), CVC3::Theorem::toString(), CVC3::TRACE, and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::isIntConst ( const Expr & e ) [virtual]

return e <=> TRUE/FALSE for e == IS_INTEGER(c), where c is a constant

Parameters:

e

is a predicate IS_INTEGER(c) where c is a rational constant

Implements CVC3::ArithProofRules.

Definition at line 2598 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::ExprManager::falseExpr(), CVC3::Expr::getRational(), CVC3::isInt(), CVC3::Rational::isInteger(), CVC3::isIntPred(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), CVC3::ExprManager::trueExpr(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::equalLeaves1 ( const Theorem & e ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 2614 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::MULT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::PLUS, CVC3::RATIONAL_EXPR, and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::equalLeaves2 ( const Theorem & e ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 2643 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::MULT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::PLUS, CVC3::RATIONAL_EXPR, and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::equalLeaves3 ( const Theorem & e ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 2672 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::MULT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::PLUS, CVC3::RATIONAL_EXPR, and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::equalLeaves4 ( const Theorem & e ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 2701 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::MULT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::PLUS, CVC3::RATIONAL_EXPR, and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::diseqToIneq ( const Theorem & diseq ) [virtual]

x /= y ==> (x < y) OR (x > y)

Used in concrete model generation

Implements CVC3::ArithProofRules.

Definition at line 2729 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::gtExpr(), CVC3::Expr::isEq(), CVC3::Expr::isNot(), CVC3::ltExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::orExpr(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::dummyTheorem ( const Expr & e ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 2748 of file arith_theorem_producer3.cpp.

References CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newRWTheorem(), and CVC3::ExprManager::trueExpr().

Theorem ArithTheoremProducer3::oneElimination ( const Expr & x ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 2753 of file arith_theorem_producer3.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::isMult(), CVC3::Expr::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::clashingBounds	(	const Theorem &	lowerBound,
		const Theorem &	upperBound
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 2774 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::add(), CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::ExprManager::falseExpr(), CVC3::Theorem::getExpr(), CVC3::Expr::getRational(), CVC3::isGE(), CVC3::isGT(), CVC3::isLE(), CVC3::isLT(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::addInequalities	(	const Theorem &	thm1,
		const Theorem &	thm2
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 2814 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Expr::getKind(), CVC3::Theorem::getProof(), CVC3::GT, CVC3::isGE(), CVC3::isGT(), CVC3::isIneq(), CVC3::isLE(), CVC3::isLT(), CVC3::LT, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::plusExpr(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::addInequalities ( const std::vector< Theorem > & thms ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 3061 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::implyWeakerInequality	(	const Expr &	expr1,
		const Expr &	expr2
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 2859 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::Expr::impExpr(), CVC3::isGE(), CVC3::isGT(), CVC3::isIneq(), CVC3::isLE(), CVC3::isLT(), CVC3::isRational(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::implyNegatedInequality	(	const Expr &	expr1,
		const Expr &	expr2
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 2906 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getRational(), CVC3::Expr::impExpr(), CVC3::isGE(), CVC3::isGT(), CVC3::isIneq(), CVC3::isLE(), CVC3::isLT(), CVC3::isRational(), CVC3::Expr::negate(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::integerSplit	(	const Expr &	intVar,
		const Rational &	intPoint
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 2951 of file arith_theorem_producer3.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::geExpr(), CVC3::IS_INTEGER, CVC3::Rational::isInteger(), CVC3::leExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::orExpr(), rat(), CVC3::Rational::toString(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::trustedRewrite	(	const Expr &	expr1,
		const Expr &	expr2
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 2938 of file arith_theorem_producer3.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), and CVC3::TheoremProducer::withProof().

Theorem ArithTheoremProducer3::rafineStrictInteger	(	const Theorem &	isIntConstrThm,
		const Expr &	constr
	)			`[virtual]`

Theorem ArithTheoremProducer3::simpleIneqInt	(	const Expr &	ineq,
		const Theorem &	isIntRHS
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 3073 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::intEqualityRationalConstant	(	const Theorem &	isIntConstrThm,
		const Expr &	constr
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 3083 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::cycleConflict ( const std::vector< Theorem > & inequalitites ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 3088 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::implyEqualities ( const std::vector< Theorem > & inequalities ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 3093 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::implyWeakerInequalityDiffLogic	(	const std::vector< Theorem > &	antecedentThms,
		const Expr &	implied
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 3029 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::implyNegatedInequalityDiffLogic	(	const std::vector< Theorem > &	antecedentThms,
		const Expr &	implied
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 3034 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::expandGrayShadowRewrite ( const Expr & theShadow ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 3039 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::compactNonLinearTerm ( const Expr & nonLinear ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 3044 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::nonLinearIneqSignSplit ( const Theorem & ineqThm ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 3049 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::implyDiffLogicBothBounds	(	const Expr &	x,
		std::vector< Theorem > &	c1_le_x,
		Rational	c1,
		std::vector< Theorem > &	x_le_c2,
		Rational	c2
	)			`[virtual]`

Implements CVC3::ArithProofRules.

Definition at line 3054 of file arith_theorem_producer3.cpp.

References DebugAssert.

Theorem ArithTheoremProducer3::powerOfOne ( const Expr & e ) [virtual]

Implements CVC3::ArithProofRules.

Definition at line 3066 of file arith_theorem_producer3.cpp.

References DebugAssert.

Member Data Documentation

TheoryArith3* CVC3::ArithTheoremProducer3::d_theoryArith [private]

Definition at line 33 of file arith_theorem_producer3.h.

Referenced by canonDivide(), canonMultConstPlus(), canonMultMtermMterm(), darkShadow(), eqElimIntRule(), grayShadow(), grayShadowConst(), intType(), intVarEqnConst(), IsIntegerElim(), and realType().

The documentation for this class was generated from the following files: