#include <core_theorem_producer.h>

Inherits CVC3::CoreProofRules, and CVC3::TheoremProducer.

Collaboration diagram for CVC3::CoreTheoremProducer:

[legend]

List of all members.

Public Member Functions

CoreTheoremProducer (TheoremManager *tm, TheoryCore *core)
virtual ~CoreTheoremProducer ()
Theorem typePred (const Expr &e)
e: T ==> |- typePred_T(e) [deriving the type predicate of e]
Theorem rewriteLetDecl (const Expr &e)
Replace LETDECL with its definition.
Theorem rewriteNotAnd (const Expr &e)
==> NOT (AND e1 ... en) IFF (OR !e1 ... !en), takes (AND ...)
Theorem rewriteNotOr (const Expr &e)
==> NOT (OR e1 ... en) IFF (AND !e1 ... !en), takes (OR ...)
Theorem rewriteNotIff (const Expr &e)
==> NOT IFF(e1,e2) IFF IFF(e1,NOT e2)
Theorem rewriteNotIte (const Expr &e)
==> NOT ITE(a,b,c) IFF ITE(a,NOT b,NOT c)
Theorem rewriteIteThen (const Expr &e, const Theorem &thenThm)
a |- b == d ==> ITE(a, b, c) == ITE(a, d, c)
Theorem rewriteIteElse (const Expr &e, const Theorem &elseThm)
!a |- c == d ==> ITE(a, b, c) == ITE(a, b, d)
Theorem rewriteIteBool (const Expr &c, const Expr &e1, const Expr &e2)
==> ITE(c, e1, e2) <=> (c => e1) AND (!c => e2)
Theorem orDistributivityRule (const Expr &e)
|= (A & B1) | (A & B2) | ... | (A & bn) <=> A & (B1 | B2 | ...| Bn)
Theorem andDistributivityRule (const Expr &e)
|= (A | B1) & (A | B2) & ... & (A | bn) <=> A | (B1 & B2 & ...& Bn)
Theorem rewriteImplies (const Expr &e)
==> IMPLIES(e1,e2) IFF OR(!e1, e2)
Theorem rewriteDistinct (const Expr &e)
==> DISTINCT(e1,...,en) IFF AND 1 <= i < j <= n (e[i] /= e[j])
Theorem NotToIte (const Expr &not_e)
==> NOT(e) == ITE(e, FALSE, TRUE)
Theorem OrToIte (const Expr &e)
==> Or(e) == ITE(e[1], TRUE, e[0])
Theorem AndToIte (const Expr &e)
==> And(e) == ITE(e[1], e[0], FALSE)
Theorem IffToIte (const Expr &e)
==> IFF(a,b) == ITE(a, b, !b)
Theorem ImpToIte (const Expr &e)
==> IMPLIES(a,b) == ITE(a, b, TRUE)
Theorem rewriteIteToNot (const Expr &e)
==> ITE(e, FALSE, TRUE) IFF NOT(e)
Theorem rewriteIteToOr (const Expr &e)
==> ITE(a, TRUE, b) IFF OR(a, b)
Theorem rewriteIteToAnd (const Expr &e)
==> ITE(a, b, FALSE) IFF AND(a, b)
Theorem rewriteIteToIff (const Expr &e)
==> ITE(a, b, !b) IFF IFF(a, b)
Theorem rewriteIteToImp (const Expr &e)
==> ITE(a, b, TRUE) IFF IMPLIES(a, b)
Theorem rewriteIteCond (const Expr &e)
==> ITE(a, b(a), c(a)) IFF ITE(a, b(TRUE), c(FALSE))
Theorem ifLiftUnaryRule (const Expr &e)
|- op(ITE(cond,a,b)) =/<=> ITE(cond,op(a),op(b))
Theorem iffOrDistrib (const Expr &iff)
((a|b)<=>(a|c))<=>(a|(b<=>c)); takes ((a|b)<=>(a|c)) as 'iff'
Theorem iffAndDistrib (const Expr &iff)
((a&b)<=>(a&c))<=>(!a|(b<=>c)); takes ((a&b)<=>(a&c)) as 'iff'
Theorem rewriteAndSubterms (const Expr &e, int idx)
(a & b) <=> a & b[a/true]; takes the index of a
Theorem rewriteOrSubterms (const Expr &e, int idx)
(a | b) <=> a | b[a/false]; takes the index of a
Theorem dummyTheorem (const Expr &e)
Temporary cheat for building theorems.

Private Attributes

TheoryCore * d_core
pointer to theory core

Detailed Description

Definition at line 40 of file core_theorem_producer.h.

Constructor & Destructor Documentation

CVC3::CoreTheoremProducer::CoreTheoremProducer	(	TheoremManager *	tm,
		TheoryCore *	core
	)		`[inline]`

Definition at line 46 of file core_theorem_producer.h.

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

Definition at line 48 of file core_theorem_producer.h.

Member Function Documentation

Theorem CoreTheoremProducer::typePred ( const Expr & e ) [virtual]

e: T ==> |- typePred_T(e) [deriving the type predicate of e]

Implements CVC3::CoreProofRules.

Definition at line 52 of file core_theorem_producer.cpp.

References CVC3::Assumptions::emptyAssump(), and CVC3::Expr::getType().

Theorem CoreTheoremProducer::rewriteLetDecl ( const Expr & e ) [virtual]

Replace LETDECL with its definition.

Used only in TheoryCore

Implements CVC3::CoreProofRules.

Definition at line 64 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getKind(), LETDECL, and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteNotAnd ( const Expr & e ) [virtual]

==> NOT (AND e1 ... en) IFF (OR !e1 ... !en), takes (AND ...)

Implements CVC3::CoreProofRules.

Definition at line 75 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::isAnd(), CVC3::Expr::isNot(), CVC3::orExpr(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteNotOr ( const Expr & e ) [virtual]

==> NOT (OR e1 ... en) IFF (AND !e1 ... !en), takes (OR ...)

Implements CVC3::CoreProofRules.

Definition at line 93 of file core_theorem_producer.cpp.

References CVC3::andExpr(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::isNot(), CVC3::Expr::isOr(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteNotIff ( const Expr & e ) [virtual]

==> NOT IFF(e1,e2) IFF IFF(e1,NOT e2)

Implements CVC3::CoreProofRules.

Definition at line 110 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isIff(), and CVC3::Expr::isNot().

Theorem CoreTheoremProducer::rewriteNotIte ( const Expr & e ) [virtual]

==> NOT ITE(a,b,c) IFF ITE(a,NOT b,NOT c)

Implements CVC3::CoreProofRules.

Definition at line 123 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isITE(), and CVC3::Expr::isNot().

Theorem CoreTheoremProducer::rewriteIteThen	(	const Expr &	e,
		const Theorem &	thenThm
	)		`[virtual]`

a |- b == d ==> ITE(a, b, c) == ITE(a, d, c)

Implements CVC3::CoreProofRules.

Definition at line 136 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, DebugAssert, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::isITE(), CVC3::Type::isNull(), CVC3::Theorem::isRewrite(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteIteElse	(	const Expr &	e,
		const Theorem &	elseThm
	)		`[virtual]`

!a |- c == d ==> ITE(a, b, c) == ITE(a, b, d)

Implements CVC3::CoreProofRules.

Definition at line 161 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, DebugAssert, CVC3::Theorem::getAssumptionsRef(), CVC3::Theorem::getExpr(), CVC3::Theorem::getLHS(), CVC3::Theorem::getProof(), CVC3::Theorem::getRHS(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::isITE(), CVC3::Type::isNull(), CVC3::Theorem::isRewrite(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteIteBool	(	const Expr &	c,
		const Expr &	e1,
		const Expr &	e2
	)		`[virtual]`

==> ITE(c, e1, e2) <=> (c => e1) AND (!c => e2)

Implements CVC3::CoreProofRules.

Definition at line 186 of file core_theorem_producer.cpp.

References CVC3::Expr::andExpr(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::iteExpr(), CVC3::Expr::orExpr(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::orDistributivityRule ( const Expr & e ) [virtual]

|= (A & B1) | (A & B2) | ... | (A & bn) <=> A & (B1 | B2 | ...| Bn)

Implements CVC3::CoreProofRules.

Definition at line 202 of file core_theorem_producer.cpp.

References CVC3::Expr::andExpr(), CVC3::Expr::arity(), CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::isAnd(), CVC3::Expr::isOr(), CVC3::orExpr(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::andDistributivityRule ( const Expr & e ) [virtual]

|= (A | B1) & (A | B2) & ... & (A | bn) <=> A | (B1 & B2 & ...& Bn)

Implements CVC3::CoreProofRules.

Definition at line 245 of file core_theorem_producer.cpp.

References CVC3::andExpr(), CVC3::Expr::arity(), CVC3::Expr::begin(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::end(), CVC3::Expr::isAnd(), CVC3::Expr::isOr(), CVC3::Expr::orExpr(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteImplies ( const Expr & e ) [virtual]

==> IMPLIES(e1,e2) IFF OR(!e1, e2)

Implements CVC3::CoreProofRules.

Definition at line 285 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), and CVC3::Expr::isImpl().

Theorem CoreTheoremProducer::rewriteDistinct ( const Expr & e ) [virtual]

==> DISTINCT(e1,...,en) IFF AND 1 <= i < j <= n (e[i] /= e[j])

Implements CVC3::CoreProofRules.

Definition at line 297 of file core_theorem_producer.cpp.

References AND, CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, DISTINCT, CVC3::Assumptions::emptyAssump(), CVC3::Expr::eqExpr(), CVC3::Expr::getEM(), CVC3::Expr::getKind(), and CVC3::ExprManager::trueExpr().

Theorem CoreTheoremProducer::NotToIte ( const Expr & not_e ) [virtual]

==> NOT(e) == ITE(e, FALSE, TRUE)

Implements CVC3::CoreProofRules.

Definition at line 328 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getType(), CVC3::Type::isBool(), and CVC3::Expr::isNot().

Theorem CoreTheoremProducer::OrToIte ( const Expr & e ) [virtual]

==> Or(e) == ITE(e[1], TRUE, e[0])

Implements CVC3::CoreProofRules.

Definition at line 345 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getKids(), CVC3::Expr::getType(), CVC3::int2string(), CVC3::Type::isNull(), CVC3::Expr::isOr(), CVC3::Expr::iteExpr(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::AndToIte ( const Expr & e ) [virtual]

==> And(e) == ITE(e[1], e[0], FALSE)

Implements CVC3::CoreProofRules.

Definition at line 383 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getKids(), CVC3::Expr::getType(), CVC3::int2string(), CVC3::Expr::isAnd(), CVC3::Type::isNull(), CVC3::Expr::iteExpr(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::IffToIte ( const Expr & e ) [virtual]

==> IFF(a,b) == ITE(a, b, !b)

Implements CVC3::CoreProofRules.

Definition at line 423 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::isIff(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::ImpToIte ( const Expr & e ) [virtual]

==> IMPLIES(a,b) == ITE(a, b, TRUE)

Implements CVC3::CoreProofRules.

Definition at line 439 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::isImpl(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteIteToNot ( const Expr & e ) [virtual]

==> ITE(e, FALSE, TRUE) IFF NOT(e)

Implements CVC3::CoreProofRules.

Definition at line 455 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isFalse(), CVC3::Expr::isITE(), CVC3::Expr::isTrue(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteIteToOr ( const Expr & e ) [virtual]

==> ITE(a, TRUE, b) IFF OR(a, b)

Implements CVC3::CoreProofRules.

Definition at line 467 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isITE(), CVC3::Expr::isTrue(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteIteToAnd ( const Expr & e ) [virtual]

==> ITE(a, b, FALSE) IFF AND(a, b)

Implements CVC3::CoreProofRules.

Definition at line 479 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isFalse(), CVC3::Expr::isITE(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteIteToIff ( const Expr & e ) [virtual]

==> ITE(a, b, !b) IFF IFF(a, b)

Implements CVC3::CoreProofRules.

Definition at line 491 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isITE(), CVC3::Expr::negate(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteIteToImp ( const Expr & e ) [virtual]

==> ITE(a, b, TRUE) IFF IMPLIES(a, b)

Implements CVC3::CoreProofRules.

Definition at line 503 of file core_theorem_producer.cpp.

References CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isITE(), CVC3::Expr::isTrue(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteIteCond ( const Expr & e ) [virtual]

==> ITE(a, b(a), c(a)) IFF ITE(a, b(TRUE), c(FALSE))

Implements CVC3::CoreProofRules.

Definition at line 516 of file core_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::isITE(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::ifLiftUnaryRule ( const Expr & e ) [virtual]

|- op(ITE(cond,a,b)) =/<=> ITE(cond,op(a),op(b))

Implements CVC3::CoreProofRules.

Definition at line 588 of file core_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getOp(), CVC3::Expr::getType(), CVC3::Type::isBool(), CVC3::Expr::isITE(), CVC3::Expr::iteExpr(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::iffOrDistrib ( const Expr & iff ) [virtual]

((a|b)<=>(a|c))<=>(a|(b<=>c)); takes ((a|b)<=>(a|c)) as 'iff'

Implements CVC3::CoreProofRules.

Definition at line 543 of file core_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::iffExpr(), CVC3::Expr::isIff(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::iffAndDistrib ( const Expr & iff ) [virtual]

((a&b)<=>(a&c))<=>(!a|(b<=>c)); takes ((a&b)<=>(a&c)) as 'iff'

Implements CVC3::CoreProofRules.

Definition at line 565 of file core_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::iffExpr(), CVC3::Expr::isIff(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteAndSubterms	(	const Expr &	e,
		int	idx
	)		`[virtual]`

(a & b) <=> a & b[a/true]; takes the index of a

and rewrites all the other conjuncts.

Implements CVC3::CoreProofRules.

Definition at line 621 of file core_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getOp(), CVC3::ExprHashMap< Data >::insert(), CVC3::int2string(), CVC3::Expr::isAnd(), and CVC3::Expr::toString().

Theorem CoreTheoremProducer::rewriteOrSubterms	(	const Expr &	e,
		int	idx
	)		`[virtual]`

(a | b) <=> a | b[a/false]; takes the index of a

and rewrites all the other disjuncts.

Implements CVC3::CoreProofRules.

Definition at line 647 of file core_theorem_producer.cpp.

References CVC3::Expr::arity(), CHECK_PROOFS, CHECK_SOUND, CVC3::Assumptions::emptyAssump(), CVC3::Expr::getOp(), CVC3::ExprHashMap< Data >::insert(), CVC3::int2string(), CVC3::Expr::isOr(), and CVC3::Expr::toString().

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

Temporary cheat for building theorems.

Implements CVC3::CoreProofRules.

Definition at line 670 of file core_theorem_producer.cpp.

References CVC3::Assumptions::emptyAssump().

Member Data Documentation

TheoryCore* CVC3::CoreTheoremProducer::d_core [private]

pointer to theory core

Definition at line 43 of file core_theorem_producer.h.

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

CVC3::CoreTheoremProducer Class Reference

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation