CVC3::CommonTheoremProducer Class Reference

#include <common_theorem_producer.h>

Inheritance diagram for CVC3::CommonTheoremProducer:

List of all members.

Public Member Functions

CommonTheoremProducer (TheoremManager *tm)
virtual ~CommonTheoremProducer ()
Theorem3 queryTCC (const Theorem &phi, const Theorem &D_phi)
Convert 2-valued formula to 3-valued by discharging its TCC ( $D_\phi$ ):

$\frac{\Gamma_1\vdash_2 \phi\quad \Gamma_2\vdash_2 D_{\phi}} {\Gamma_1,\,\Gamma_2\vdash_3\phi}$

.
Theorem3 implIntro3 (const Theorem3 &phi, const std::vector< Expr > &assump, const std::vector< Theorem > &tccs)
3-valued implication introduction rule:

$\frac{\Gamma_0,\,\alpha_1\,\ldots,\,\alpha_n\vdash_3\phi\quad (\Gamma_i\vdash D_{\alpha_i})_{i\in[1..n]}} {\Gamma_0,\,\Gamma_1, \ldots, \Gamma_n\vdash_3 (\bigwedge_{i=1}^n\alpha_i)\to\phi}$
Theorem assumpRule (const Expr &a, int scope=-1)
$\frac{}{a\vdash a}$
Theorem reflexivityRule (const Expr &a)
$\frac{}{a = a}\quad or \quad\frac{}{a \Leftrightarrow a}$
Theorem rewriteReflexivity (const Expr &t)
==> (a == a) IFF TRUE
Theorem symmetryRule (const Theorem &a1_eq_a2)
$\frac{a_1=a_2}{a_2=a_1}$

(same for IFF)
Theorem rewriteUsingSymmetry (const Expr &a1_eq_a2)
$\frac{}{(a_1=a_2)\Leftrightarrow (a_2=a_1)}$
Theorem transitivityRule (const Theorem &a1_eq_a2, const Theorem &a2_eq_a3)
$\frac{a_1=a_2\quad a_2=a_3}{a_1=a_3}$

(same for IFF)
Theorem substitutivityRule (const Expr &e, const Theorem &thm)
Optimized case for expr with one child.
Theorem substitutivityRule (const Expr &e, const Theorem &thm1, const Theorem &thm2)
Optimized case for expr with two children.
Theorem substitutivityRule (const Op &op, const std::vector< Theorem > &thms)
$\frac{(c_1=d_1)\wedge\ldots\wedge(c_n=d_n)} {op(c_1,\ldots,c_n)=op(d_1,\ldots,d_n)}$
Theorem substitutivityRule (const Expr &e, const std::vector< unsigned > &changed, const std::vector< Theorem > &thms)
$\frac{(c_1=d_1)\wedge\ldots\wedge(c_n=d_n)} {op(c_1,\ldots,c_n)=op(d_1,\ldots,d_n)}$

except that only those arguments are given that $c_i\not=d_i$ .
Theorem substitutivityRule (const Expr &e, const int changed, const Theorem &thm)
Theorem contradictionRule (const Theorem &e, const Theorem &not_e)
$\frac{\Gamma_1\vdash e\quad\Gamma_2\vdash \neg e} {\Gamma_1\cup\Gamma_2\vdash \mathrm{FALSE}}$
Theorem excludedMiddle (const Expr &e)
Theorem iffTrue (const Theorem &e)
$\frac{\Gamma\vdash e}{\Gamma\vdash e\Leftrightarrow\mathrm{TRUE}}$
Theorem iffNotFalse (const Theorem &e)
$\frac{\Gamma\vdash e}{\Gamma\vdash\neg e\Leftrightarrow\mathrm{FALSE}}$
Theorem iffTrueElim (const Theorem &e)
$\frac{\Gamma\vdash e\Leftrightarrow\mathrm{TRUE}}{\Gamma\vdash e}$
Theorem iffFalseElim (const Theorem &e)
$\frac{\Gamma\vdash e\Leftrightarrow\mathrm{FALSE}}{\Gamma\vdash\neg e}$
Theorem iffContrapositive (const Theorem &thm)
e1 <=> e2 ==> ~e1 <=> ~e2
Theorem notNotElim (const Theorem &e)
$\frac{\Gamma\vdash\neg\neg e}{\Gamma\vdash e}$
Theorem iffMP (const Theorem &e1, const Theorem &e1_iff_e2)
$\frac{\Gamma_1\vdash e_1\quad \Gamma_2\vdash(e_1\Leftrightarrow e_2)} {\Gamma_1\cup\Gamma_2\vdash e_2}$
Theorem implMP (const Theorem &e1, const Theorem &e1_impl_e2)
$\frac{\Gamma_1\vdash e_1\quad \Gamma_2\vdash(e_1\Rightarrow e_2)} {\Gamma_1\cup\Gamma_2\vdash e_2}$
Theorem andElim (const Theorem &e, int i)
$\frac{\vdash e_1\wedge\cdots\wedge e_n}{\vdash e_i}$
Theorem andIntro (const Theorem &e1, const Theorem &e2)
e1, e2 ==> AND(e1, e2)
Theorem andIntro (const std::vector< Theorem > &es)
$\frac{\Gamma_1\vdash e_1\quad \cdots \quad\Gamma_n\vdash e_n} {\bigcup_{i=1}^n\Gamma_i\vdash \bigwedge_{i=1}^n e_i}$
Theorem implIntro (const Theorem &phi, const std::vector< Expr > &assump)
Implication introduction rule:

$\frac{\Gamma,\,\alpha_1\,\ldots,\,\alpha_n\vdash\phi} {\Gamma\vdash(\bigwedge_{i=1}^n\alpha_i)\to\phi}$

.
Theorem implContrapositive (const Theorem &thm)
e1 => e2 ==> ~e2 => ~e1
Theorem rewriteIteTrue (const Expr &e)
==> ITE(TRUE, e1, e2) == e1
Theorem rewriteIteFalse (const Expr &e)
==> ITE(FALSE, e1, e2) == e2
Theorem rewriteIteSame (const Expr &e)
==> ITE(c, e, e) == e
Theorem notToIff (const Theorem &not_e)
$\frac{\vdash\neg e}{\vdash e\Leftrightarrow\mathrm{FALSE}}$
Theorem xorToIff (const Expr &e)
$\frac{\vdash e_1 XOR e_2}{\vdash e_1\Leftrightarrow(\neg e_2)}$
Theorem rewriteIff (const Expr &e)
==> (e1 <=> e2) <=> [simplified expr]
Theorem rewriteAnd (const Expr &e)
==> AND(e1,e2) IFF [simplified expr]
Theorem rewriteOr (const Expr &e)
==> OR(e1,...,en) IFF [simplified expr]
Theorem rewriteNotTrue (const Expr &e)
==> NOT TRUE IFF FALSE
Theorem rewriteNotFalse (const Expr &e)
==> NOT FALSE IFF TRUE
Theorem rewriteNotNot (const Expr &e)
==> NOT NOT e IFF e, takes !!e
Theorem rewriteNotForall (const Expr &forallExpr)
==> NOT FORALL (vars): e IFF EXISTS (vars) NOT e
Theorem rewriteNotExists (const Expr &existsExpr)
==> NOT EXISTS (vars): e IFF FORALL (vars) NOT e
Expr skolemize (const Expr &e)
Theorem skolemizeRewrite (const Expr &e)
Theorem skolemizeRewriteVar (const Expr &e)
Special version of skolemizeRewrite for "EXISTS x. t = x".
Theorem varIntroRule (const Expr &e)
|- EXISTS x. e = x
Theorem skolemize (const Theorem &thm)
If thm is (EXISTS x: phi(x)), create the Skolemized version and add it to the database. Otherwise returns just thm.
Theorem varIntroSkolem (const Expr &e)
Retrun a theorem "|- e = v" for a new Skolem constant v.
Theorem trueTheorem ()
==> TRUE
Theorem rewriteAnd (const Theorem &e)
AND(e1,e2) ==> [simplified expr].
Theorem rewriteOr (const Theorem &e)
OR(e1,...,en) ==> [simplified expr].
Theorem ackermann (const Expr &e1, const Expr &e2)
Theorem liftOneITE (const Expr &e)
std::vector< Theorem > & getSkolemAxioms ()
void clearSkolemAxioms ()

Private Member Functions

void findITE (const Expr &e, Expr &condition, Expr &thenpart, Expr &elsepart)
Helper function for liftOneITE.

Private Attributes

std::vector< Theorem > d_skolem_axioms
CDMap< Expr, Theorem > d_skolemized_thms
CDMap< Expr, Theorem > d_skolemVars
Mapping of e to "|- e = v" for fresh Skolem vars v.

Detailed Description

Definition at line 40 of file common_theorem_producer.h.

Constructor & Destructor Documentation

CommonTheoremProducer::CommonTheoremProducer ( TheoremManager * tm )

Definition at line 40 of file common_theorem_producer.cpp.

virtual CVC3::CommonTheoremProducer::~CommonTheoremProducer ( ) [inline, virtual]

Definition at line 60 of file common_theorem_producer.h.

Member Function Documentation

void CommonTheoremProducer::findITE	(	const Expr &	e,
		Expr &	condition,
		Expr &	thenpart,
		Expr &	elsepart
	)			`[private]`

Helper function for liftOneITE.

Definition at line 1322 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Expr::containsTermITE(), CVC3::Expr::getOp(), CVC3::Expr::getType(), CVC3::Type::isBool(), and CVC3::Expr::isITE().

Referenced by liftOneITE().

Theorem3 CommonTheoremProducer::queryTCC	(	const Theorem &	phi,
		const Theorem &	D_phi
	)			`[virtual]`

Convert 2-valued formula to 3-valued by discharging its TCC ( $D_\phi$ ):

$\frac{\Gamma_1\vdash_2 \phi\quad \Gamma_2\vdash_2 D_{\phi}} {\Gamma_1,\,\Gamma_2\vdash_3\phi}$

.

Implements CVC3::CommonProofRules.

Definition at line 55 of file common_theorem_producer.cpp.

References CVC3::Assumptions::add(), CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem3(), and CVC3::TheoremProducer::withProof().

Theorem3 CommonTheoremProducer::implIntro3	(	const Theorem3 &	phi,
		const std::vector< Expr > &	assump,
		const std::vector< Theorem > &	tccs
	)			`[virtual]`

3-valued implication introduction rule:

$\frac{\Gamma_0,\,\alpha_1\,\ldots,\,\alpha_n\vdash_3\phi\quad (\Gamma_i\vdash D_{\alpha_i})_{i\in[1..n]}} {\Gamma_0,\,\Gamma_1, \ldots, \Gamma_n\vdash_3 (\bigwedge_{i=1}^n\alpha_i)\to\phi}$

Parameters:

	phi	is the formula $\phi$
	assump	is the vector of assumptions $\alpha_1\ldots\alpha_n$
	tccs	is the vector of TCCs for assumptions $D_{\alpha_1}\ldots D_{\alpha_n}$

Implements CVC3::CommonProofRules.

Definition at line 85 of file common_theorem_producer.cpp.

References CVC3::Assumptions::add(), CVC3::andExpr(), CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem3::getAssumptionsRef(), CVC3::Theorem3::getExpr(), CVC3::Theorem3::getProof(), CVC3::Theorem::getProof(), CVC3::Expr::impExpr(), CVC3::int2string(), CVC3::Theorem::isAssump(), CVC3::Theorem::isNull(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem3(), CVC3::Expr::toString(), CVC3::TheoremProducer::withAssumptions(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::assumpRule	(	const Expr &	a,
		int	scope = `-1`
	)			`[virtual]`

$\frac{}{a\vdash a}$

Implements CVC3::CommonProofRules.

Definition at line 154 of file common_theorem_producer.cpp.

References CVC3::TheoremProducer::newAssumption(), CVC3::TheoremProducer::newLabel(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::reflexivityRule ( const Expr & a ) [virtual]

$\frac{}{a = a}\quad or \quad\frac{}{a \Leftrightarrow a}$

Implements CVC3::CommonProofRules.

Definition at line 162 of file common_theorem_producer.cpp.

References CVC3::TheoremProducer::newReflTheorem().

Referenced by rewriteIff(), rewriteUsingSymmetry(), substitutivityRule(), symmetryRule(), transitivityRule(), and trueTheorem().

Theorem CommonTheoremProducer::rewriteReflexivity ( const Expr & a_eq_a ) [virtual]

==> (a == a) IFF TRUE

Implements CVC3::CommonProofRules.

Definition at line 168 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isEq(), CVC3::Expr::isIff(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), CVC3::ExprManager::trueExpr(), and CVC3::TheoremProducer::withProof().

Referenced by rewriteIff().

Theorem CommonTheoremProducer::symmetryRule ( const Theorem & a1_eq_a2 ) [virtual]

$\frac{a_1=a_2}{a_2=a_1}$

(same for IFF)

Implements CVC3::CommonProofRules.

Definition at line 187 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Type::getExpr(), CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::Expr::getType(), IF_DEBUG, CVC3::Type::isBool(), CVC3::Theorem::isRewrite(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), reflexivityRule(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteUsingSymmetry ( const Expr & a1_eq_a2 ) [virtual]

$\frac{}{(a_1=a_2)\Leftrightarrow (a_2=a_1)}$

Implements CVC3::CommonProofRules.

Definition at line 221 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::Type::getExpr(), CVC3::Expr::iffExpr(), CVC3::Expr::isEq(), CVC3::Expr::isIff(), CVC3::Type::isNull(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), reflexivityRule(), and CVC3::TheoremProducer::withProof().

Referenced by rewriteIff().

Theorem CommonTheoremProducer::transitivityRule	(	const Theorem &	a1_eq_a2,
		const Theorem &	a2_eq_a3
	)			`[virtual]`

$\frac{a_1=a_2\quad a_2=a_3}{a_1=a_3}$

(same for IFF)

Implements CVC3::CommonProofRules.

Definition at line 245 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, DebugAssert, CVC3::Type::getExpr(), CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Type::isNull(), CVC3::Theorem::isNull(), CVC3::Theorem::isRewrite(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), reflexivityRule(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::substitutivityRule	(	const Expr &	e,
		const Theorem &	thm
	)			`[virtual]`

Optimized case for expr with one child.

Implements CVC3::CommonProofRules.

Definition at line 302 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Expr::getOp(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), IF_DEBUG, CVC3::Theorem::isRefl(), CVC3::Theorem::isRewrite(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Theorem::setSubst(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Referenced by substitutivityRule().

Theorem CommonTheoremProducer::substitutivityRule	(	const Expr &	e,
		const Theorem &	thm1,
		const Theorem &	thm2
	)			`[virtual]`

Optimized case for expr with two children.

Implements CVC3::CommonProofRules.

Definition at line 332 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Expr::getOp(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), IF_DEBUG, CVC3::Theorem::isRefl(), CVC3::Theorem::isRewrite(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Theorem::setSubst(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::substitutivityRule	(	const Op &	op,
		const std::vector< Theorem > &	thms
	)			`[virtual]`

$\frac{(c_1=d_1)\wedge\ldots\wedge(c_n=d_n)} {op(c_1,\ldots,c_n)=op(d_1,\ldots,d_n)}$

Implements CVC3::CommonProofRules.

Definition at line 373 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_tm, CVC3::TheoremManager::getEM(), IF_DEBUG, CVC3::ExprManager::newLeafExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), reflexivityRule(), CVC3::Theorem::setSubst(), CVC3::Op::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::substitutivityRule	(	const Expr &	e,
		const std::vector< unsigned > &	changed,
		const std::vector< Theorem > &	thms
	)			`[virtual]`

$\frac{(c_1=d_1)\wedge\ldots\wedge(c_n=d_n)} {op(c_1,\ldots,c_n)=op(d_1,\ldots,d_n)}$

except that only those arguments are given that $c_i\not=d_i$ .

Parameters:

	e	is the original expression $op(c_1,\ldots,c_n)$ .
	changed	is the vector of indices of changed kids
	thms	are the theorems for the changed kids.

Implements CVC3::CommonProofRules.

Definition at line 424 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, DebugAssert, CVC3::Expr::getOp(), IF_DEBUG, CVC3::Theorem::isRefl(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), reflexivityRule(), CVC3::Theorem::setSubst(), substitutivityRule(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::substitutivityRule	(	const Expr &	e,
		const int	changed,
		const Theorem &	thm
	)			`[virtual]`

Theorem CommonTheoremProducer::contradictionRule	(	const Theorem &	e,
		const Theorem &	not_e
	)			`[virtual]`

$\frac{\Gamma_1\vdash e\quad\Gamma_2\vdash \neg e} {\Gamma_1\cup\Gamma_2\vdash \mathrm{FALSE}}$

Implements CVC3::CommonProofRules.

Definition at line 561 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::ExprManager::falseExpr(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::excludedMiddle ( const Expr & e ) [virtual]

Implements CVC3::CommonProofRules.

Definition at line 580 of file common_theorem_producer.cpp.

References CVC3::Assumptions::emptyAssump(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::orExpr(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::iffTrue ( const Theorem & e ) [virtual]

$\frac{\Gamma\vdash e}{\Gamma\vdash e\Leftrightarrow\mathrm{TRUE}}$

Implements CVC3::CommonProofRules.

Definition at line 591 of file common_theorem_producer.cpp.

References CVC3::TheoremProducer::d_em, CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::ExprManager::trueExpr(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::iffNotFalse ( const Theorem & e ) [virtual]

$\frac{\Gamma\vdash e}{\Gamma\vdash\neg e\Leftrightarrow\mathrm{FALSE}}$

Implements CVC3::CommonProofRules.

Definition at line 602 of file common_theorem_producer.cpp.

References CVC3::TheoremProducer::d_em, CVC3::ExprManager::falseExpr(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::iffTrueElim ( const Theorem & e ) [virtual]

$\frac{\Gamma\vdash e\Leftrightarrow\mathrm{TRUE}}{\Gamma\vdash e}$

Implements CVC3::CommonProofRules.

Definition at line 612 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::Theorem::isRewrite(), CVC3::Expr::isTrue(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Referenced by trueTheorem().

Theorem CommonTheoremProducer::iffFalseElim ( const Theorem & e ) [virtual]

$\frac{\Gamma\vdash e\Leftrightarrow\mathrm{FALSE}}{\Gamma\vdash\neg e}$

Implements CVC3::CommonProofRules.

Definition at line 626 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::Expr::isFalse(), CVC3::Theorem::isRewrite(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::iffContrapositive ( const Theorem & thm ) [virtual]

e1 <=> e2 ==> ~e1 <=> ~e2

$\frac{\Gamma\vdash e_1\Leftrightarrow e_2} {\Gamma\vdash\sim e_1\Leftrightarrow\sim e_2}$

Where ~e is the inverse of e (that is, ~(!e') = e').

Implements CVC3::CommonProofRules.

Definition at line 641 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Theorem::isRewrite(), CVC3::Expr::negate(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::notNotElim ( const Theorem & not_not_e ) [virtual]

$\frac{\Gamma\vdash\neg\neg e}{\Gamma\vdash e}$

Implements CVC3::CommonProofRules.

Definition at line 655 of file common_theorem_producer.cpp.

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

Theorem CommonTheoremProducer::iffMP	(	const Theorem &	e1,
		const Theorem &	e1_iff_e2
	)			`[virtual]`

$\frac{\Gamma_1\vdash e_1\quad \Gamma_2\vdash(e_1\Leftrightarrow e_2)} {\Gamma_1\cup\Gamma_2\vdash e_2}$

Implements CVC3::CommonProofRules.

Definition at line 667 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::Theorem::isRewrite(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Referenced by rewriteAnd(), rewriteOr(), skolemize(), and varIntroSkolem().

Theorem CommonTheoremProducer::implMP	(	const Theorem &	e1,
		const Theorem &	e1_impl_e2
	)			`[virtual]`

$\frac{\Gamma_1\vdash e_1\quad \Gamma_2\vdash(e_1\Rightarrow e_2)} {\Gamma_1\cup\Gamma_2\vdash e_2}$

Implements CVC3::CommonProofRules.

Definition at line 692 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::isImpl(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Theorem::toString(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::andElim	(	const Theorem &	e,
		int	i
	)			`[virtual]`

$\frac{\vdash e_1\wedge\cdots\wedge e_n}{\vdash e_i}$

Implements CVC3::CommonProofRules.

Definition at line 718 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::int2string(), CVC3::Expr::isAnd(), CVC3::TheoremProducer::newPf(), CVC3::ExprManager::newRatExpr(), CVC3::TheoremProducer::newTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::andIntro	(	const Theorem &	e1,
		const Theorem &	e2
	)			`[virtual]`

e1, e2 ==> AND(e1, e2)

Implements CVC3::CommonProofRules.

Definition at line 733 of file common_theorem_producer.cpp.

Theorem CommonTheoremProducer::andIntro ( const std::vector< Theorem > & es ) [virtual]

$\frac{\Gamma_1\vdash e_1\quad \cdots \quad\Gamma_n\vdash e_n} {\bigcup_{i=1}^n\Gamma_i\vdash \bigwedge_{i=1}^n e_i}$

Implements CVC3::CommonProofRules.

Definition at line 741 of file common_theorem_producer.cpp.

References CVC3::andExpr(), CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::implIntro	(	const Theorem &	phi,
		const std::vector< Expr > &	assump
	)			`[virtual]`

Implication introduction rule:

$\frac{\Gamma,\,\alpha_1\,\ldots,\,\alpha_n\vdash\phi} {\Gamma\vdash(\bigwedge_{i=1}^n\alpha_i)\to\phi}$

.

Parameters:

	phi	is the formula $\phi$
	assump	is the vector of assumptions $\alpha_1\ldots\alpha_n$

Implements CVC3::CommonProofRules.

Definition at line 775 of file common_theorem_producer.cpp.

References CVC3::andExpr(), CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::impExpr(), CVC3::int2string(), CVC3::Theorem::isAssump(), CVC3::Theorem::isNull(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::toString(), CVC3::TheoremProducer::withAssumptions(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::implContrapositive ( const Theorem & thm ) [virtual]

e1 => e2 ==> ~e2 => ~e1

$\frac{\Gamma\vdash e_1\Rightarrow e_2} {\Gamma\vdash\sim e_2\Rightarrow\sim e_1}$

Where ~e is the inverse of e (that is, ~(!e') = e').

Implements CVC3::CommonProofRules.

Definition at line 825 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::isImpl(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteIteTrue ( const Expr & e ) [virtual]

==> ITE(TRUE, e1, e2) == e1

Implements CVC3::CommonProofRules.

Definition at line 841 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Type::getExpr(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::isITE(), CVC3::Type::isNull(), CVC3::Expr::isTrue(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteIteFalse ( const Expr & e ) [virtual]

==> ITE(FALSE, e1, e2) == e2

Implements CVC3::CommonProofRules.

Definition at line 863 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Type::getExpr(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::isFalse(), CVC3::Expr::isITE(), CVC3::Type::isNull(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteIteSame ( const Expr & e ) [virtual]

==> ITE(c, e, e) == e

Implements CVC3::CommonProofRules.

Definition at line 885 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, DebugAssert, CVC3::Assumptions::emptyAssump(), CVC3::Type::getExpr(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::isITE(), CVC3::Type::isNull(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::notToIff ( const Theorem & not_e ) [virtual]

$\frac{\vdash\neg e}{\vdash e\Leftrightarrow\mathrm{FALSE}}$

Implements CVC3::CommonProofRules.

Definition at line 906 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::ExprManager::falseExpr(), CVC3::Theorem::getExpr(), CVC3::Theorem::getProof(), CVC3::Expr::isNot(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Theorem::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::xorToIff ( const Expr & e ) [virtual]

$\frac{\vdash e_1 XOR e_2}{\vdash e_1\Leftrightarrow(\neg e_2)}$

Implements CVC3::CommonProofRules.

Definition at line 922 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isXor(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteIff ( const Expr & e ) [virtual]

==> (e1 <=> e2) <=> [simplified expr]

Rewrite formulas like FALSE/TRUE <=> e, e <=> NOT e, etc.

Implements CVC3::CommonProofRules.

Definition at line 941 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::FALSE_EXPR, CVC3::ExprManager::falseExpr(), CVC3::Expr::isIff(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::NOT, reflexivityRule(), rewriteReflexivity(), rewriteUsingSymmetry(), CVC3::TRUE_EXPR, and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteAnd ( const Expr & e ) [virtual]

==> AND(e1,e2) IFF [simplified expr]

Implements CVC3::CommonProofRules.

Definition at line 989 of file common_theorem_producer.cpp.

References CVC3::andExpr(), CVC3::Expr::arity(), CVC3::ExprMap< Data >::begin(), CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CVC3::ExprMap< Data >::count(), CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::ExprMap< Data >::end(), CVC3::Expr::end(), CVC3::ExprManager::falseExpr(), CVC3::Expr::isAnd(), CVC3::Expr::isFalse(), CVC3::Expr::isTrue(), CVC3::Expr::negate(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::ExprMap< Data >::size(), CVC3::Expr::toString(), CVC3::ExprManager::trueExpr(), and CVC3::TheoremProducer::withProof().

Referenced by rewriteAnd().

Theorem CommonTheoremProducer::rewriteOr ( const Expr & e ) [virtual]

==> OR(e1,...,en) IFF [simplified expr]

Implements CVC3::CommonProofRules.

Definition at line 1028 of file common_theorem_producer.cpp.

References CVC3::Expr::arity(), CVC3::ExprMap< Data >::begin(), CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CVC3::ExprMap< Data >::count(), CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::ExprMap< Data >::end(), CVC3::Expr::end(), CVC3::ExprManager::falseExpr(), CVC3::Expr::isFalse(), CVC3::Expr::isOr(), CVC3::Expr::isTrue(), CVC3::Expr::negate(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::orExpr(), CVC3::ExprMap< Data >::size(), CVC3::Expr::toString(), CVC3::ExprManager::trueExpr(), and CVC3::TheoremProducer::withProof().

Referenced by rewriteOr().

Theorem CommonTheoremProducer::rewriteNotTrue ( const Expr & e ) [virtual]

==> NOT TRUE IFF FALSE

Implements CVC3::CommonProofRules.

Definition at line 1066 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::ExprManager::falseExpr(), CVC3::Expr::isNot(), CVC3::Expr::isTrue(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteNotFalse ( const Expr & e ) [virtual]

==> NOT FALSE IFF TRUE

Implements CVC3::CommonProofRules.

Definition at line 1078 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isFalse(), CVC3::Expr::isNot(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::ExprManager::trueExpr(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteNotNot ( const Expr & e ) [virtual]

==> NOT NOT e IFF e, takes !!e

Implements CVC3::CommonProofRules.

Definition at line 1090 of file common_theorem_producer.cpp.

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

Theorem CommonTheoremProducer::rewriteNotForall ( const Expr & forallExpr ) [virtual]

==> NOT FORALL (vars): e IFF EXISTS (vars) NOT e

Implements CVC3::CommonProofRules.

Definition at line 1102 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::EXISTS, CVC3::Expr::getBody(), CVC3::Expr::getVars(), CVC3::Expr::isForall(), CVC3::Expr::isNot(), CVC3::ExprManager::newClosureExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::rewriteNotExists ( const Expr & existsExpr ) [virtual]

==> NOT EXISTS (vars): e IFF FORALL (vars) NOT e

Implements CVC3::CommonProofRules.

Definition at line 1117 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::FORALL, CVC3::Expr::getBody(), CVC3::Expr::getVars(), CVC3::Expr::isExists(), CVC3::Expr::isNot(), CVC3::ExprManager::newClosureExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Expr CommonTheoremProducer::skolemize ( const Expr & e ) [virtual]

Implements CVC3::CommonProofRules.

Definition at line 1131 of file common_theorem_producer.cpp.

References CVC3::Expr::getBody(), CVC3::Expr::getVars(), CVC3::Expr::skolemExpr(), and CVC3::Expr::substExpr().

Referenced by skolemizeRewrite().

Theorem CommonTheoremProducer::skolemizeRewrite ( const Expr & e ) [virtual]

skolem rewrite rule: Introduces axiom |- Exists(x) phi(x) <=> phi(c) where c is a constant defined by the expression Exists(x) phi(x)

Implements CVC3::CommonProofRules.

Definition at line 1145 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::iffExpr(), CVC3::Expr::isExists(), CVC3::TheoremProducer::newLabel(), CVC3::TheoremProducer::newRWTheorem(), skolemize(), CVC3::Expr::toString(), CVC3::TRACE, and CVC3::TheoremProducer::withProof().

Referenced by skolemize().

Theorem CommonTheoremProducer::skolemizeRewriteVar ( const Expr & e ) [virtual]

Special version of skolemizeRewrite for "EXISTS x. t = x".

Implements CVC3::CommonProofRules.

Definition at line 1165 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getBody(), CVC3::Expr::getOp(), CVC3::Expr::getVars(), CVC3::Expr::iffExpr(), CVC3::Expr::isEq(), CVC3::Expr::isExists(), CVC3::Expr::isIff(), CVC3::TheoremProducer::newLabel(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::skolemExpr(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

Referenced by varIntroSkolem().

Theorem CommonTheoremProducer::varIntroRule ( const Expr & e ) [virtual]

|- EXISTS x. e = x

Implements CVC3::CommonProofRules.

Definition at line 1202 of file common_theorem_producer.cpp.

References CVC3::TheoremProducer::d_em, CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::EXISTS, CVC3::Expr::getType(), CVC3::Expr::iffExpr(), CVC3::Type::isBool(), CVC3::ExprManager::newBoundVarExpr(), CVC3::ExprManager::newClosureExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), and CVC3::TheoremProducer::withProof().

Referenced by varIntroSkolem().

Theorem CommonTheoremProducer::skolemize ( const Theorem & thm ) [virtual]

If thm is (EXISTS x: phi(x)), create the Skolemized version and add it to the database. Otherwise returns just thm.

Parameters:

thm

is the Theorem(EXISTS x: phi(x))

Implements CVC3::CommonProofRules.

Definition at line 1223 of file common_theorem_producer.cpp.

References d_skolem_axioms, d_skolemized_thms, CVC3::CDMap< Key, Data, HashFcn >::end(), CVC3::CDMap< Key, Data, HashFcn >::find(), CVC3::Theorem::getExpr(), CVC3::Expr::getVars(), iffMP(), CVC3::CDMap< Key, Data, HashFcn >::insert(), CVC3::Expr::isExists(), CVC3::Expr::skolemExpr(), skolemizeRewrite(), and CVC3::TRACE.

Theorem CommonTheoremProducer::varIntroSkolem ( const Expr & e ) [virtual]

Retrun a theorem "|- e = v" for a new Skolem constant v.

This is equivalent to skolemize(d_core->varIntroRule(e)), only more efficient.

Implements CVC3::CommonProofRules.

Definition at line 1250 of file common_theorem_producer.cpp.

References d_skolem_axioms, d_skolemized_thms, d_skolemVars, DebugAssert, CVC3::CDMap< Key, Data, HashFcn >::end(), CVC3::CDMap< Key, Data, HashFcn >::find(), CVC3::Theorem::getExpr(), CVC3::Expr::getVars(), iffMP(), CVC3::CDMap< Key, Data, HashFcn >::insert(), CVC3::Expr::isExists(), skolemizeRewriteVar(), CVC3::Expr::toString(), and varIntroRule().

Theorem CommonTheoremProducer::trueTheorem ( ) [virtual]

==> TRUE

Implements CVC3::CommonProofRules.

Definition at line 1280 of file common_theorem_producer.cpp.

References CVC3::TheoremProducer::d_em, iffTrueElim(), reflexivityRule(), and CVC3::ExprManager::trueExpr().

Theorem CommonTheoremProducer::rewriteAnd ( const Theorem & e ) [virtual]

AND(e1,e2) ==> [simplified expr].

Implements CVC3::CommonProofRules.

Definition at line 1286 of file common_theorem_producer.cpp.

References CVC3::Theorem::getExpr(), iffMP(), and rewriteAnd().

Theorem CommonTheoremProducer::rewriteOr ( const Theorem & e ) [virtual]

OR(e1,...,en) ==> [simplified expr].

Implements CVC3::CommonProofRules.

Definition at line 1292 of file common_theorem_producer.cpp.

References CVC3::Theorem::getExpr(), iffMP(), and rewriteOr().

Theorem CommonTheoremProducer::ackermann	(	const Expr &	e1,
		const Expr &	e2
	)			`[virtual]`

Implements CVC3::CommonProofRules.

Definition at line 1298 of file common_theorem_producer.cpp.

References CVC3::AND, CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::Expr::getOp(), CVC3::Expr::isApply(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newTheorem(), and CVC3::TheoremProducer::withProof().

Theorem CommonTheoremProducer::liftOneITE ( const Expr & e ) [virtual]

Implements CVC3::CommonProofRules.

Definition at line 1359 of file common_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Expr::containsTermITE(), CVC3::Assumptions::emptyAssump(), findITE(), CVC3::Expr::iteExpr(), CVC3::TheoremProducer::newPf(), CVC3::TheoremProducer::newRWTheorem(), CVC3::Expr::toString(), and CVC3::TheoremProducer::withProof().

std::vector<Theorem>& CVC3::CommonTheoremProducer::getSkolemAxioms ( ) [inline, virtual]

Implements CVC3::CommonProofRules.

Definition at line 126 of file common_theorem_producer.h.

References d_skolem_axioms.

void CVC3::CommonTheoremProducer::clearSkolemAxioms ( ) [inline, virtual]

Implements CVC3::CommonProofRules.

Definition at line 127 of file common_theorem_producer.h.

References d_skolem_axioms.

Member Data Documentation

std::vector<Theorem> CVC3::CommonTheoremProducer::d_skolem_axioms [private]

Definition at line 46 of file common_theorem_producer.h.

Referenced by clearSkolemAxioms(), getSkolemAxioms(), skolemize(), and varIntroSkolem().

CDMap<Expr, Theorem> CVC3::CommonTheoremProducer::d_skolemized_thms [private]

Definition at line 50 of file common_theorem_producer.h.

Referenced by skolemize(), and varIntroSkolem().

CDMap<Expr, Theorem> CVC3::CommonTheoremProducer::d_skolemVars [private]

Mapping of e to "|- e = v" for fresh Skolem vars v.

Definition at line 53 of file common_theorem_producer.h.

Referenced by varIntroSkolem().

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