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/******************************************************************************
* Top contributors (to current version):
* Mudathir Mohamed
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* bag reduction.
*/
#include "theory/bags/bag_reduction.h"
#include "expr/bound_var_manager.h"
#include "expr/emptybag.h"
#include "expr/skolem_manager.h"
#include "theory/quantifiers/fmf/bounded_integers.h"
#include "util/rational.h"
using namespace cvc5;
using namespace cvc5::kind;
namespace cvc5 {
namespace theory {
namespace bags {
BagReduction::BagReduction(Env& env) : EnvObj(env) {}
BagReduction::~BagReduction() {}
/**
* A bound variable corresponding to the universally quantified integer
* variable used to range over (may be distinct) elements in a bag, used
* for axiomatizing the behavior of some term.
* If there are multiple quantifiers, this variable should be the first one.
*/
struct FirstIndexVarAttributeId
{
};
typedef expr::Attribute<FirstIndexVarAttributeId, Node> FirstIndexVarAttribute;
/**
* A bound variable corresponding to the universally quantified integer
* variable used to range over (may be distinct) elements in a bag, used
* for axiomatizing the behavior of some term.
* This variable should be the second of multiple quantifiers.
*/
struct SecondIndexVarAttributeId
{
};
typedef expr::Attribute<SecondIndexVarAttributeId, Node>
SecondIndexVarAttribute;
Node BagReduction::reduceFoldOperator(Node node, std::vector<Node>& asserts)
{
Assert(node.getKind() == BAG_FOLD);
if (d_env.getLogicInfo().isHigherOrder())
{
NodeManager* nm = NodeManager::currentNM();
SkolemManager* sm = nm->getSkolemManager();
Node f = node[0];
Node t = node[1];
Node A = node[2];
Node zero = nm->mkConstInt(Rational(0));
Node one = nm->mkConstInt(Rational(1));
// types
TypeNode bagType = A.getType();
TypeNode elementType = A.getType().getBagElementType();
TypeNode integerType = nm->integerType();
TypeNode ufType = nm->mkFunctionType(integerType, elementType);
TypeNode resultType = t.getType();
TypeNode combineType = nm->mkFunctionType(integerType, resultType);
TypeNode unionDisjointType = nm->mkFunctionType(integerType, bagType);
// skolem functions
Node n = sm->mkSkolemFunction(SkolemFunId::BAGS_FOLD_CARD, integerType, A);
Node uf = sm->mkSkolemFunction(SkolemFunId::BAGS_FOLD_ELEMENTS, ufType, A);
Node unionDisjoint = sm->mkSkolemFunction(
SkolemFunId::BAGS_FOLD_UNION_DISJOINT, unionDisjointType, A);
Node combine = sm->mkSkolemFunction(
SkolemFunId::BAGS_FOLD_COMBINE, combineType, {f, t, A});
BoundVarManager* bvm = nm->getBoundVarManager();
Node i =
bvm->mkBoundVar<FirstIndexVarAttribute>(node, "i", nm->integerType());
Node iList = nm->mkNode(BOUND_VAR_LIST, i);
Node iMinusOne = nm->mkNode(MINUS, i, one);
Node uf_i = nm->mkNode(APPLY_UF, uf, i);
Node combine_0 = nm->mkNode(APPLY_UF, combine, zero);
Node combine_iMinusOne = nm->mkNode(APPLY_UF, combine, iMinusOne);
Node combine_i = nm->mkNode(APPLY_UF, combine, i);
Node combine_n = nm->mkNode(APPLY_UF, combine, n);
Node unionDisjoint_0 = nm->mkNode(APPLY_UF, unionDisjoint, zero);
Node unionDisjoint_iMinusOne =
nm->mkNode(APPLY_UF, unionDisjoint, iMinusOne);
Node unionDisjoint_i = nm->mkNode(APPLY_UF, unionDisjoint, i);
Node unionDisjoint_n = nm->mkNode(APPLY_UF, unionDisjoint, n);
Node combine_0_equal = combine_0.eqNode(t);
Node combine_i_equal =
combine_i.eqNode(nm->mkNode(APPLY_UF, f, uf_i, combine_iMinusOne));
Node unionDisjoint_0_equal =
unionDisjoint_0.eqNode(nm->mkConst(EmptyBag(bagType)));
Node singleton = nm->mkBag(elementType, uf_i, one);
Node unionDisjoint_i_equal = unionDisjoint_i.eqNode(
nm->mkNode(BAG_UNION_DISJOINT, singleton, unionDisjoint_iMinusOne));
Node interval_i =
nm->mkNode(AND, nm->mkNode(GEQ, i, one), nm->mkNode(LEQ, i, n));
Node body_i =
nm->mkNode(IMPLIES,
interval_i,
nm->mkNode(AND, combine_i_equal, unionDisjoint_i_equal));
Node forAll_i =
quantifiers::BoundedIntegers::mkBoundedForall(iList, body_i);
Node nonNegative = nm->mkNode(GEQ, n, zero);
Node unionDisjoint_n_equal = A.eqNode(unionDisjoint_n);
asserts.push_back(forAll_i);
asserts.push_back(combine_0_equal);
asserts.push_back(unionDisjoint_0_equal);
asserts.push_back(unionDisjoint_n_equal);
asserts.push_back(nonNegative);
return combine_n;
}
return Node::null();
}
Node BagReduction::reduceCardOperator(Node node, std::vector<Node>& asserts)
{
Assert(node.getKind() == BAG_CARD);
NodeManager* nm = NodeManager::currentNM();
SkolemManager* sm = nm->getSkolemManager();
Node A = node[0];
Node zero = nm->mkConst(CONST_RATIONAL, Rational(0));
Node one = nm->mkConst(CONST_RATIONAL, Rational(1));
// types
TypeNode bagType = A.getType();
TypeNode elementType = A.getType().getBagElementType();
TypeNode integerType = nm->integerType();
TypeNode ufType = nm->mkFunctionType(integerType, elementType);
TypeNode cardinalityType = nm->mkFunctionType(integerType, integerType);
TypeNode unionDisjointType = nm->mkFunctionType(integerType, bagType);
// skolem functions
Node n = sm->mkSkolemFunction(SkolemFunId::BAGS_CARD_N, integerType, A);
Node uf = sm->mkSkolemFunction(SkolemFunId::BAGS_CARD_ELEMENTS, ufType, A);
Node unionDisjoint = sm->mkSkolemFunction(
SkolemFunId::BAGS_CARD_UNION_DISJOINT, unionDisjointType, A);
Node cardinality = sm->mkSkolemFunction(
SkolemFunId::BAGS_CARD_CARDINALITY, cardinalityType, A);
BoundVarManager* bvm = nm->getBoundVarManager();
Node i =
bvm->mkBoundVar<FirstIndexVarAttribute>(node, "i", nm->integerType());
Node j =
bvm->mkBoundVar<SecondIndexVarAttribute>(node, "j", nm->integerType());
Node iList = nm->mkNode(BOUND_VAR_LIST, i);
Node jList = nm->mkNode(BOUND_VAR_LIST, j);
Node iMinusOne = nm->mkNode(MINUS, i, one);
Node uf_i = nm->mkNode(APPLY_UF, uf, i);
Node uf_j = nm->mkNode(APPLY_UF, uf, j);
Node cardinality_0 = nm->mkNode(APPLY_UF, cardinality, zero);
Node cardinality_iMinusOne = nm->mkNode(APPLY_UF, cardinality, iMinusOne);
Node cardinality_i = nm->mkNode(APPLY_UF, cardinality, i);
Node cardinality_n = nm->mkNode(APPLY_UF, cardinality, n);
Node unionDisjoint_0 = nm->mkNode(APPLY_UF, unionDisjoint, zero);
Node unionDisjoint_iMinusOne = nm->mkNode(APPLY_UF, unionDisjoint, iMinusOne);
Node unionDisjoint_i = nm->mkNode(APPLY_UF, unionDisjoint, i);
Node unionDisjoint_n = nm->mkNode(APPLY_UF, unionDisjoint, n);
Node cardinality_0_equal = cardinality_0.eqNode(zero);
Node uf_i_multiplicity = nm->mkNode(BAG_COUNT, uf_i, A);
Node cardinality_i_equal = cardinality_i.eqNode(
nm->mkNode(PLUS, uf_i_multiplicity, cardinality_iMinusOne));
Node unionDisjoint_0_equal =
unionDisjoint_0.eqNode(nm->mkConst(EmptyBag(bagType)));
Node bag = nm->mkBag(elementType, uf_i, uf_i_multiplicity);
Node unionDisjoint_i_equal = unionDisjoint_i.eqNode(
nm->mkNode(BAG_UNION_DISJOINT, bag, unionDisjoint_iMinusOne));
// 1 <= i <= n
Node interval_i =
nm->mkNode(AND, nm->mkNode(GEQ, i, one), nm->mkNode(LEQ, i, n));
// i < j <= n
Node interval_j =
nm->mkNode(AND, nm->mkNode(LT, i, j), nm->mkNode(LEQ, j, n));
// uf(i) != uf(j)
Node uf_i_equals_uf_j = nm->mkNode(EQUAL, uf_i, uf_j);
Node notEqual = nm->mkNode(EQUAL, uf_i, uf_j).negate();
Node body_j = nm->mkNode(OR, interval_j.negate(), notEqual);
Node forAll_j = quantifiers::BoundedIntegers::mkBoundedForall(jList, body_j);
Node body_i = nm->mkNode(
IMPLIES,
interval_i,
nm->mkNode(AND, cardinality_i_equal, unionDisjoint_i_equal, forAll_j));
Node forAll_i = quantifiers::BoundedIntegers::mkBoundedForall(iList, body_i);
Node nonNegative = nm->mkNode(GEQ, n, zero);
Node unionDisjoint_n_equal = A.eqNode(unionDisjoint_n);
asserts.push_back(forAll_i);
asserts.push_back(cardinality_0_equal);
asserts.push_back(unionDisjoint_0_equal);
asserts.push_back(unionDisjoint_n_equal);
asserts.push_back(nonNegative);
return cardinality_n;
}
} // namespace bags
} // namespace theory
} // namespace cvc5
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