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/******************************************************************************
* Top contributors (to current version):
* Mudathir Mohamed, Andrew Reynolds, Gereon Kremer
*
* 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.
* ****************************************************************************
*
* Inference generator utility.
*/
#include "cvc5_private.h"
#ifndef CVC5__THEORY__BAGS__INFERENCE_GENERATOR_H
#define CVC5__THEORY__BAGS__INFERENCE_GENERATOR_H
#include "expr/node.h"
#include "infer_info.h"
namespace cvc5 {
namespace theory {
namespace bags {
class InferenceManager;
class SolverState;
/**
* An inference generator class. This class is used by the core solver to
* generate lemmas
*/
class InferenceGenerator
{
public:
InferenceGenerator(SolverState* state, InferenceManager* im);
/**
* @param A is a bag of type (Bag E)
* @param e is a node of type E
* @return an inference that represents the following implication
* (=>
* true
* (>= (bag.count e A) 0)
*/
InferInfo nonNegativeCount(Node n, Node e);
/**
* @param n is (bag x c) of type (Bag E)
* @param e is a node of type E
* @return an inference that represents the following cases:
* 1- e, x are in the same equivalent class, then we infer:
* (= (bag.count e skolem) (ite (>= c 1) c 0)))
* 2- e, x are known to be disequal, then we infer:
* (= (bag.count e skolem) 0))
* 3- if neither holds, we infer:
* (= (bag.count e skolem) (ite (and (= e x) (>= c 1)) c 0)))
* where skolem = (bag x c) is a fresh variable
*/
InferInfo mkBag(Node n, Node e);
/**
* @param n is (= A B) where A, B are bags of type (Bag E), and
* (not (= A B)) is an assertion in the equality engine
* @return an inference that represents the following implication
* (=>
* (not (= A B))
* (not (= (count e A) (count e B))))
* where e is a fresh skolem of type E.
*/
InferInfo bagDisequality(Node n);
/**
* @param n is (as emptybag (Bag E))
* @param e is a node of Type E
* @return an inference that represents the following implication
* (=>
* true
* (= 0 (count e skolem)))
* where skolem = (as emptybag (Bag String))
*/
InferInfo empty(Node n, Node e);
/**
* @param n is (union_disjoint A B) where A, B are bags of type (Bag E)
* @param e is a node of Type E
* @return an inference that represents the following implication
* (=>
* true
* (= (count e skolem)
* (+ (count e A) (count e B))))
* where skolem is a fresh variable equals (union_disjoint A B)
*/
InferInfo unionDisjoint(Node n, Node e);
/**
* @param n is (union_disjoint A B) where A, B are bags of type (Bag E)
* @param e is a node of Type E
* @return an inference that represents the following implication
* (=>
* true
* (=
* (count e skolem)
* (ite
* (> (count e A) (count e B))
* (count e A)
* (count e B)))))
* where skolem is a fresh variable equals (union_max A B)
*/
InferInfo unionMax(Node n, Node e);
/**
* @param n is (intersection_min A B) where A, B are bags of type (Bag E)
* @param e is a node of Type E
* @return an inference that represents the following implication
* (=>
* true
* (=
* (count e skolem)
* (ite(
* (< (count e A) (count e B))
* (count e A)
* (count e B)))))
* where skolem is a fresh variable equals (intersection_min A B)
*/
InferInfo intersection(Node n, Node e);
/**
* @param n is (difference_subtract A B) where A, B are bags of type (Bag E)
* @param e is a node of Type E
* @return an inference that represents the following implication
* (=>
* true
* (=
* (count e skolem)
* (ite
* (>= (count e A) (count e B))
* (- (count e A) (count e B))
* 0))))
* where skolem is a fresh variable equals (difference_subtract A B)
*/
InferInfo differenceSubtract(Node n, Node e);
/**
* @param n is (difference_remove A B) where A, B are bags of type (Bag E)
* @param e is a node of Type E
* @return an inference that represents the following implication
* (=>
* true
* (=
* (count e skolem)
* (ite
* (<= (count e B) 0)
* (count e A)
* 0))))
* where skolem is a fresh variable equals (difference_remove A B)
*/
InferInfo differenceRemove(Node n, Node e);
/**
* @param n is (duplicate_removal A) where A is a bag of type (Bag E)
* @param e is a node of Type E
* @return an inference that represents the following implication
* (=>
* true
* (=
* (count e skolem)
* (ite (>= (count e A) 1) 1 0))))
* where skolem is a fresh variable equals (duplicate_removal A)
*/
InferInfo duplicateRemoval(Node n, Node e);
/**
* @param n is (bag.map f A) where f is a function (-> E T), A a bag of type
* (Bag E)
* @param e is a node of Type E
* @return an inference that represents the following implication
* (and
* (= (sum 0) 0)
* (= (sum preImageSize) (bag.count e skolem))
* (>= preImageSize 0)
* (forall ((i Int))
* (let ((uf_i (uf i)))
* (let ((count_uf_i (bag.count uf_i A)))
* (=>
* (and (>= i 1) (<= i preImageSize))
* (and
* (= (f uf_i) e)
* (>= count_uf_i 1)
* (= (sum i) (+ (sum (- i 1)) count_uf_i))
* (forall ((j Int))
* (or
* (not (and (< i j) (<= j preImageSize)))
* (not (= (uf i) (uf j)))) )
* ))))))
* where uf: Int -> E is an uninterpreted function from integers to the
* type of the elements of A
* preImageSize is the cardinality of the distinct elements in A that are
* mapped to e by function f (i.e., preimage of {e})
* sum: Int -> Int is a function that aggregates the multiplicities of the
* preimage of e,
* and skolem is a fresh variable equals (bag.map f A))
*/
std::tuple<InferInfo, Node, Node> mapDownwards(Node n, Node e);
/**
* @param n is (bag.map f A) where f is a function (-> E T), A a bag of type
* (Bag E)
* @param uf is an uninterpreted function Int -> E
* @param preImageSize is the cardinality of the distinct elements in A that
* are mapped to y by function f (i.e., preimage of {y})
* @param y is an element of type T
* @param e is an element of type E
* @return an inference that represents the following implication
* (=>
* (>= (bag.count x A) 1)
* (or
* (not (= (f x) y)
* (and
* (>= skolem 1)
* (<= skolem preImageSize)
* (= (uf skolem) x)))))
* where skolem is a fresh variable
*/
InferInfo mapUpwards(Node n, Node uf, Node preImageSize, Node y, Node x);
/**
* @param element of type T
* @param bag of type (bag T)
* @return a count term (bag.count element bag)
*/
Node getMultiplicityTerm(Node element, Node bag);
private:
/** generate skolem variable for node n and add it to inferInfo */
Node getSkolem(Node& n, InferInfo& inferInfo);
NodeManager* d_nm;
SkolemManager* d_sm;
SolverState* d_state;
/** Pointer to the inference manager */
InferenceManager* d_im;
/** Commonly used constants */
Node d_true;
Node d_zero;
Node d_one;
};
} // namespace bags
} // namespace theory
} // namespace cvc5
#endif /* CVC5__THEORY__BAGS__INFERENCE_GENERATOR_H */
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