Proof Rules for the Search Engines
[Search Engine]

Collaboration diagram for Proof Rules for the Search Engines:

Classes

class CVCL::SearchEngineRules
API to the proof rules for the Search Engines. More...

Functions

virtual CVCL::SearchEngineRules::~SearchEngineRules ()
Destructor.
virtual Theorem CVCL::SearchEngineRules::eliminateSkolemAxioms (const Theorem &tFalse, const std::vector< Theorem > &delta)=0
virtual Theorem CVCL::SearchEngineRules::proofByContradiction (const Expr &a, const Theorem &pfFalse)=0
Proof by contradiction:
$\frac{\Gamma, \neg A \vdash\mathrm{FALSE}}{\Gamma \vdash A}$
.
virtual Theorem CVCL::SearchEngineRules::negIntro (const Expr &not_a, const Theorem &pfFalse)=0
Negation introduction:
$\frac{\Gamma, A \vdash\mathrm{FALSE}}{\Gamma\vdash\neg A}$
.
virtual Theorem CVCL::SearchEngineRules::caseSplit (const Expr &a, const Theorem &a_proves_c, const Theorem &not_a_proves_c)=0
Case split:
$\frac{\Gamma_1, A\vdash C \quad \Gamma_2, \neg A\vdash C} {\Gamma_1\cup\Gamma_2\vdash C}$
.
virtual Theorem CVCL::SearchEngineRules::conflictClause (const Theorem &thm, const std::vector< Theorem > &lits, const std::vector< Theorem > &gamma)=0
Conflict clause rule:
$\frac{\Gamma,A_1,\ldots,A_n\vdash\mathrm{FALSE}} {\Gamma\vdash\neg A_1\vee\cdots\vee \neg A_n}$
.
virtual Theorem CVCL::SearchEngineRules::cutRule (const std::vector< Theorem > &thmsA, const Theorem &as_prove_b)=0
Cut rule:
$\frac{\Gamma_1\vdash A_1\quad\cdots\quad\Gamma_n\vdash A_n \quad \Gamma', A_1,\ldots,A_n\vdash B} {\bigcup_{i=1}^n\Gamma_i\cup\Gamma'\vdash B}$
.
virtual Theorem CVCL::SearchEngineRules::unitProp (const std::vector< Theorem > &thms, const Theorem &clause, unsigned i)=0
Unit propagation rule:
$\frac{\Gamma_j\vdash\neg A_j\mbox{ for }j\in[1\ldots n]-\{i\} \quad \Gamma\vdash A_1\vee\cdots\vee A_n} {\bigcup_{j\in[1\ldots n]-\{i\}}\Gamma_j\cup\Gamma\vdash A_i}$
.
virtual Theorem CVCL::SearchEngineRules::conflictRule (const std::vector< Theorem > &thms, const Theorem &clause)=0
"Conflict" rule (all literals in a clause become FALSE)
$\frac{\Gamma_j\vdash\neg A_j\mbox{ for }j\in[1\ldots n] \quad \Gamma\vdash A_1\vee\cdots\vee A_n} {\bigcup_{j\in[1\ldots n]}\Gamma_j\cup\Gamma \vdash\mathrm{FALSE}}$
virtual Theorem CVCL::SearchEngineRules::propAndrAF (const Theorem &andr_th, bool left, const Theorem &b_th)=0
virtual Theorem CVCL::SearchEngineRules::propAndrAT (const Theorem &andr_th, const Theorem &l_th, const Theorem &r_th)=0
virtual void CVCL::SearchEngineRules::propAndrLRT (const Theorem &andr_th, const Theorem &a_th, Theorem *l_th, Theorem *r_th)=0
virtual Theorem CVCL::SearchEngineRules::propAndrLF (const Theorem &andr_th, const Theorem &a_th, const Theorem &r_th)=0
virtual Theorem CVCL::SearchEngineRules::propAndrRF (const Theorem &andr_th, const Theorem &a_th, const Theorem &l_th)=0
virtual Theorem CVCL::SearchEngineRules::confAndrAT (const Theorem &andr_th, const Theorem &a_th, bool left, const Theorem &b_th)=0
virtual Theorem CVCL::SearchEngineRules::confAndrAF (const Theorem &andr_th, const Theorem &a_th, const Theorem &l_th, const Theorem &r_th)=0
virtual Theorem CVCL::SearchEngineRules::propIffr (const Theorem &iffr_th, int p, const Theorem &a_th, const Theorem &b_th)=0
virtual Theorem CVCL::SearchEngineRules::confIffr (const Theorem &iffr_th, const Theorem &i_th, const Theorem &l_th, const Theorem &r_th)=0
virtual Theorem CVCL::SearchEngineRules::propIterIte (const Theorem &iter_th, bool left, const Theorem &if_th, const Theorem &then_th)=0
virtual void CVCL::SearchEngineRules::propIterIfThen (const Theorem &iter_th, bool left, const Theorem &ite_th, const Theorem &then_th, Theorem *if_th, Theorem *else_th)=0
virtual Theorem CVCL::SearchEngineRules::propIterThen (const Theorem &iter_th, const Theorem &ite_th, const Theorem &if_th)=0
virtual Theorem CVCL::SearchEngineRules::confIterThenElse (const Theorem &iter_th, const Theorem &ite_th, const Theorem &then_th, const Theorem &else_th)=0
virtual Theorem CVCL::SearchEngineRules::confIterIfThen (const Theorem &iter_th, bool left, const Theorem &ite_th, const Theorem &if_th, const Theorem &then_th)=0
virtual Theorem CVCL::SearchEngineRules::andCNFRule (const Theorem &thm)=0
AND(x1,...,xn) <=> v |- CNF[AND(x1,...,xn) <=> v].
virtual Theorem CVCL::SearchEngineRules::orCNFRule (const Theorem &thm)=0
OR(x1,...,xn) <=> v |- CNF[OR(x1,...,xn) <=> v].
virtual Theorem CVCL::SearchEngineRules::impCNFRule (const Theorem &thm)=0
(x1 => x2) <=> v |- CNF[(x1 => x2) <=> v]
virtual Theorem CVCL::SearchEngineRules::iffCNFRule (const Theorem &thm)=0
(x1 <=> x2) <=> v |- CNF[(x1 <=> x2) <=> v]
virtual Theorem CVCL::SearchEngineRules::iteCNFRule (const Theorem &thm)=0
ITE(c, x1, x2) <=> v |- CNF[ITE(c, x1, x2) <=> v].
virtual Theorem CVCL::SearchEngineRules::iteToClauses (const Theorem &ite)=0
ITE(c, f1, f2) |- (NOT c OR f1) AND (c OR f2).
virtual Theorem CVCL::SearchEngineRules::iffToClauses (const Theorem &iff)=0
e1 <=> e2 |- (NOT e1 OR e2) AND (e1 OR NOT e2)

Function Documentation

virtual CVCL::SearchEngineRules::~SearchEngineRules ( ) [inline, virtual, inherited]

Destructor.

Definition at line 49 of file search_rules.h.

virtual Theorem CVCL::SearchEngineRules::eliminateSkolemAxioms ( const Theorem & tFalse,

const std::vector< Theorem > & delta

) [pure virtual, inherited]

Eliminate skolem axioms: Gamma, Delta |- false => Gamma|- false where Delta is a set of skolem axioms {|-Exists(x) phi (x) => phi(c)} and gamma does not contain any of the skolem constants c.
Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::processResult().

virtual Theorem CVCL::SearchEngineRules::proofByContradiction ( const Expr & a,

const Theorem & pfFalse

) [pure virtual, inherited]

Proof by contradiction:
$\frac{\Gamma, \neg A \vdash\mathrm{FALSE}}{\Gamma \vdash A}$
.
$\neg A$ does not have to be present in the assumptions.
Parameters:

a is the assumption A

pfFalse is the theorem $\Gamma, \neg A \vdash\mathrm{FALSE}$

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::processResult().

virtual Theorem CVCL::SearchEngineRules::negIntro ( const Expr & not_a,

const Theorem & pfFalse

) [pure virtual, inherited]

Negation introduction:
$\frac{\Gamma, A \vdash\mathrm{FALSE}}{\Gamma\vdash\neg A}$
.

Parameters:

not_a is the formula $\neg A$ . We pass the negation $\neg A$ , and not just A, for efficiency: building $\neg A$ is more expensive (due to uniquifying pointers in Expr package) than extracting A from $\neg A$ .

pfFalse is the theorem $\Gamma, A \vdash\mathrm{FALSE}$

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::processResult().

virtual Theorem CVCL::SearchEngineRules::caseSplit ( const Expr & a,

const Theorem & a_proves_c,

const Theorem & not_a_proves_c

) [pure virtual, inherited]

Case split:
$\frac{\Gamma_1, A\vdash C \quad \Gamma_2, \neg A\vdash C} {\Gamma_1\cup\Gamma_2\vdash C}$
.

Parameters:

a is the assumption A to split on

a_proves_c is the theorem $\Gamma_1, A\vdash C$

not_a_proves_c is the theorem $\Gamma_2, \neg A\vdash C$

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchSimple::checkValidRec().

virtual Theorem CVCL::SearchEngineRules::conflictClause ( const Theorem & thm,

const std::vector< Theorem > & lits,

const std::vector< Theorem > & gamma

) [pure virtual, inherited]

Conflict clause rule:
$\frac{\Gamma,A_1,\ldots,A_n\vdash\mathrm{FALSE}} {\Gamma\vdash\neg A_1\vee\cdots\vee \neg A_n}$
.

Parameters:

thm is the theorem $\Gamma,A_1,\ldots,A_n\vdash\mathrm{FALSE}$

lits is the vector of literals A_i. They must be present in the set of assumptions of thm.

gamma FIXME: document this!!

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchEngineFast::analyzeUIPs().

virtual Theorem CVCL::SearchEngineRules::cutRule ( const std::vector< Theorem > & thmsA,

const Theorem & as_prove_b

) [pure virtual, inherited]

Cut rule:
$\frac{\Gamma_1\vdash A_1\quad\cdots\quad\Gamma_n\vdash A_n \quad \Gamma', A_1,\ldots,A_n\vdash B} {\bigcup_{i=1}^n\Gamma_i\cup\Gamma'\vdash B}$
.

Parameters:

thmsA is a vector of theorems $\Gamma_i\vdash A_i$

as_prove_b is the theorem $\Gamma', A_1,\ldots,A_n\vdash B$ (the name means "A's prove B")

Implemented in CVCL::SearchEngineTheoremProducer.

virtual Theorem CVCL::SearchEngineRules::unitProp ( const std::vector< Theorem > & thms,

const Theorem & clause,

unsigned i

) [pure virtual, inherited]

Unit propagation rule:
$\frac{\Gamma_j\vdash\neg A_j\mbox{ for }j\in[1\ldots n]-\{i\} \quad \Gamma\vdash A_1\vee\cdots\vee A_n} {\bigcup_{j\in[1\ldots n]-\{i\}}\Gamma_j\cup\Gamma\vdash A_i}$
.

Parameters:

clause is the proof of the clause $\Gamma\vdash A_1\vee\cdots\vee A_n$

i is the index (0..n-1) of the literal to be unit-propagated

thms is the vector of theorems $\Gamma_j\vdash\neg A_j$ for all literals except A_i

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchEngineFast::addNonLiteralFact(), CVCL::Variable::deriveThmRec(), and CVCL::SearchEngineFast::unitPropagation().

virtual Theorem CVCL::SearchEngineRules::conflictRule ( const std::vector< Theorem > & thms,

const Theorem & clause

) [pure virtual, inherited]

"Conflict" rule (all literals in a clause become FALSE)
$\frac{\Gamma_j\vdash\neg A_j\mbox{ for }j\in[1\ldots n] \quad \Gamma\vdash A_1\vee\cdots\vee A_n} {\bigcup_{j\in[1\ldots n]}\Gamma_j\cup\Gamma \vdash\mathrm{FALSE}}$

Parameters:

clause is the proof of the clause $\Gamma\vdash A_1\vee\cdots\vee A_n$

thms is the vector of theorems $\Gamma_j\vdash\neg A_j$

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchEngineFast::addNonLiteralFact(), CVCL::Variable::deriveThmRec(), and CVCL::SearchEngineFast::propagate().

virtual Theorem CVCL::SearchEngineRules::propAndrAF ( const Theorem & andr_th,

bool left,

const Theorem & b_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::propAndrAT ( const Theorem & andr_th,

const Theorem & l_th,

const Theorem & r_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual void CVCL::SearchEngineRules::propAndrLRT ( const Theorem & andr_th,

const Theorem & a_th,

Theorem * l_th,

Theorem * r_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::propAndrLF ( const Theorem & andr_th,

const Theorem & a_th,

const Theorem & r_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::propAndrRF ( const Theorem & andr_th,

const Theorem & a_th,

const Theorem & l_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::confAndrAT ( const Theorem & andr_th,

const Theorem & a_th,

bool left,

const Theorem & b_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::confAndrAF ( const Theorem & andr_th,

const Theorem & a_th,

const Theorem & l_th,

const Theorem & r_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::propIffr ( const Theorem & iffr_th,

int p,

const Theorem & a_th,

const Theorem & b_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::confIffr ( const Theorem & iffr_th,

const Theorem & i_th,

const Theorem & l_th,

const Theorem & r_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::propIterIte ( const Theorem & iter_th,

bool left,

const Theorem & if_th,

const Theorem & then_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual void CVCL::SearchEngineRules::propIterIfThen ( const Theorem & iter_th,

bool left,

const Theorem & ite_th,

const Theorem & then_th,

Theorem * if_th,

Theorem * else_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::propIterThen ( const Theorem & iter_th,

const Theorem & ite_th,

const Theorem & if_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::confIterThenElse ( const Theorem & iter_th,

const Theorem & ite_th,

const Theorem & then_th,

const Theorem & else_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::confIterIfThen ( const Theorem & iter_th,

bool left,

const Theorem & ite_th,

const Theorem & if_th,

const Theorem & then_th

) [pure virtual, inherited]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::Circuit::propagate().

virtual Theorem CVCL::SearchEngineRules::andCNFRule ( const Theorem & thm ) [pure virtual, inherited]

AND(x1,...,xn) <=> v |- CNF[AND(x1,...,xn) <=> v].

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::applyCNFRules().

virtual Theorem CVCL::SearchEngineRules::orCNFRule ( const Theorem & thm ) [pure virtual, inherited]

OR(x1,...,xn) <=> v |- CNF[OR(x1,...,xn) <=> v].

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::applyCNFRules().

virtual Theorem CVCL::SearchEngineRules::impCNFRule ( const Theorem & thm ) [pure virtual, inherited]

(x1 => x2) <=> v |- CNF[(x1 => x2) <=> v]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::applyCNFRules().

virtual Theorem CVCL::SearchEngineRules::iffCNFRule ( const Theorem & thm ) [pure virtual, inherited]

(x1 <=> x2) <=> v |- CNF[(x1 <=> x2) <=> v]

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::applyCNFRules().

virtual Theorem CVCL::SearchEngineRules::iteCNFRule ( const Theorem & thm ) [pure virtual, inherited]

ITE(c, x1, x2) <=> v |- CNF[ITE(c, x1, x2) <=> v].

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::applyCNFRules().

virtual Theorem CVCL::SearchEngineRules::iteToClauses ( const Theorem & ite ) [pure virtual, inherited]

ITE(c, f1, f2) |- (NOT c OR f1) AND (c OR f2).

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::enqueueCNFrec().

virtual Theorem CVCL::SearchEngineRules::iffToClauses ( const Theorem & iff ) [pure virtual, inherited]

e1 <=> e2 |- (NOT e1 OR e2) AND (e1 OR NOT e2)

Implemented in CVCL::SearchEngineTheoremProducer.
Referenced by CVCL::SearchImplBase::applyCNFRules().

Generated on Thu Apr 13 16:57:40 2006 for CVC Lite by

1.4.4

Proof Rules for the Search Engines [Search Engine]

Classes

Functions

Function Documentation

Proof Rules for the Search Engines
[Search Engine]