CVC3: CVC3::SearchEngineRules Class Reference

API to the proof rules for the Search Engines. More...

#include <search_rules.h>

Inherited by CVC3::SearchEngineTheoremProducer.

List of all members.

Public Member Functions

virtual ~SearchEngineRules ()
Destructor.
virtual Theorem eliminateSkolemAxioms (const Theorem &tFalse, const std::vector< Theorem > &delta)=0
virtual Theorem proofByContradiction (const Expr &a, const Theorem &pfFalse)=0
Proof by contradiction:

$\frac{\Gamma, \neg A \vdash\mathrm{FALSE}}{\Gamma \vdash A}$

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virtual Theorem negIntro (const Expr &not_a, const Theorem &pfFalse)=0
Negation introduction:

$\frac{\Gamma, A \vdash\mathrm{FALSE}}{\Gamma\vdash\neg A}$

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virtual Theorem caseSplit (const Expr &a, const Theorem &a_proves_c, const Theorem &not_a_proves_c)=0
Case split:

$\frac{\Gamma_1, A\vdash C \quad \Gamma_2, \neg A\vdash C} {\Gamma_1\cup\Gamma_2\vdash C}$

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virtual Theorem conflictClause (const Theorem &thm, const std::vector< Theorem > &lits, const std::vector< Theorem > &gamma)=0
Conflict clause rule:

$\frac{\Gamma,A_1,\ldots,A_n\vdash\mathrm{FALSE}} {\Gamma\vdash\neg A_1\vee\cdots\vee \neg A_n}$

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virtual Theorem cutRule (const std::vector< Theorem > &thmsA, const Theorem &as_prove_b)=0
Cut rule:

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

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virtual Theorem unitProp (const std::vector< Theorem > &thms, const Theorem &clause, unsigned i)=0
Unit propagation rule:

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

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virtual Theorem 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 propAndrAF (const Theorem &andr_th, bool left, const Theorem &b_th)=0
virtual Theorem propAndrAT (const Theorem &andr_th, const Theorem &l_th, const Theorem &r_th)=0
virtual void propAndrLRT (const Theorem &andr_th, const Theorem &a_th, Theorem *l_th, Theorem *r_th)=0
virtual Theorem propAndrLF (const Theorem &andr_th, const Theorem &a_th, const Theorem &r_th)=0
virtual Theorem propAndrRF (const Theorem &andr_th, const Theorem &a_th, const Theorem &l_th)=0
virtual Theorem confAndrAT (const Theorem &andr_th, const Theorem &a_th, bool left, const Theorem &b_th)=0
virtual Theorem confAndrAF (const Theorem &andr_th, const Theorem &a_th, const Theorem &l_th, const Theorem &r_th)=0
virtual Theorem propIffr (const Theorem &iffr_th, int p, const Theorem &a_th, const Theorem &b_th)=0
virtual Theorem confIffr (const Theorem &iffr_th, const Theorem &i_th, const Theorem &l_th, const Theorem &r_th)=0
virtual Theorem propIterIte (const Theorem &iter_th, bool left, const Theorem &if_th, const Theorem &then_th)=0
virtual void propIterIfThen (const Theorem &iter_th, bool left, const Theorem &ite_th, const Theorem &then_th, Theorem *if_th, Theorem *else_th)=0
virtual Theorem propIterThen (const Theorem &iter_th, const Theorem &ite_th, const Theorem &if_th)=0
virtual Theorem confIterThenElse (const Theorem &iter_th, const Theorem &ite_th, const Theorem &then_th, const Theorem &else_th)=0
virtual Theorem confIterIfThen (const Theorem &iter_th, bool left, const Theorem &ite_th, const Theorem &if_th, const Theorem &then_th)=0
virtual Theorem andCNFRule (const Theorem &thm)=0
AND(x1,...,xn) <=> v |- CNF[AND(x1,...,xn) <=> v].
virtual Theorem orCNFRule (const Theorem &thm)=0
OR(x1,...,xn) <=> v |- CNF[OR(x1,...,xn) <=> v].
virtual Theorem impCNFRule (const Theorem &thm)=0
(x1 => x2) <=> v |- CNF[(x1 => x2) <=> v]
virtual Theorem iffCNFRule (const Theorem &thm)=0
(x1 <=> x2) <=> v |- CNF[(x1 <=> x2) <=> v]
virtual Theorem iteCNFRule (const Theorem &thm)=0
ITE(c, x1, x2) <=> v |- CNF[ITE(c, x1, x2) <=> v].
virtual Theorem iteToClauses (const Theorem &ite)=0
ITE(c, f1, f2) |- (NOT c OR f1) AND (c OR f2)
virtual Theorem iffToClauses (const Theorem &iff)=0
e1 <=> e2 |- (NOT e1 OR e2) AND (e1 OR NOT e2)
virtual Theorem satProof (const Expr &queryExpr, const Proof &satProof)=0

Detailed Description

API to the proof rules for the Search Engines.

Definition at line 35 of file search_rules.h.

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

search_rules.h

CVC3::SearchEngineRules Class ReferenceProof Rules for the Search Engines

Public Member Functions

Detailed Description

CVC3::SearchEngineRules Class Reference
Proof Rules for the Search Engines