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/********************* */
/*! \file proof_equality_engine.cpp
** \verbatim
** Top contributors (to current version):
** Andrew Reynolds, Gereon Kremer
** This file is part of the CVC4 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.\endverbatim
**
** \brief Implementation of the proof-producing equality engine
**/
#include "theory/uf/proof_equality_engine.h"
#include "expr/lazy_proof_chain.h"
#include "expr/proof_node.h"
#include "expr/proof_node_manager.h"
#include "theory/rewriter.h"
#include "theory/uf/eq_proof.h"
#include "theory/uf/equality_engine.h"
#include "theory/uf/proof_checker.h"
using namespace cvc5::kind;
namespace cvc5 {
namespace theory {
namespace eq {
ProofEqEngine::ProofEqEngine(context::Context* c,
context::UserContext* u,
EqualityEngine& ee,
ProofNodeManager* pnm)
: EagerProofGenerator(pnm, u, "pfee::" + ee.identify()),
d_ee(ee),
d_factPg(c, pnm),
d_pnm(pnm),
d_proof(pnm, nullptr, c, "pfee::LazyCDProof::" + ee.identify()),
d_keep(c)
{
NodeManager* nm = NodeManager::currentNM();
d_true = nm->mkConst(true);
d_false = nm->mkConst(false);
AlwaysAssert(pnm != nullptr)
<< "Should not construct ProofEqEngine without proof node manager";
}
bool ProofEqEngine::assertFact(Node lit,
PfRule id,
const std::vector<Node>& exp,
const std::vector<Node>& args)
{
Trace("pfee") << "pfee::assertFact " << lit << " " << id << ", exp = " << exp
<< ", args = " << args << std::endl;
Node atom = lit.getKind() == NOT ? lit[0] : lit;
bool polarity = lit.getKind() != NOT;
// register the step in the proof
if (holds(atom, polarity))
{
// we do not process this fact if it already holds
return false;
}
// Buffer the step in the fact proof generator. We do this instead of
// adding explict steps to the lazy proof d_proof since CDProof has
// (at most) one proof for each formula. Thus, we "claim" only the
// formula that is proved by this fact. Otherwise, aliasing may occur,
// which leads to cyclic or bogus proofs.
ProofStep ps;
ps.d_rule = id;
ps.d_children = exp;
ps.d_args = args;
d_factPg.addStep(lit, ps);
// add lazy step to proof
d_proof.addLazyStep(lit, &d_factPg);
// second, assert it to the equality engine
Node reason = NodeManager::currentNM()->mkAnd(exp);
return assertFactInternal(atom, polarity, reason);
}
bool ProofEqEngine::assertFact(Node lit,
PfRule id,
Node exp,
const std::vector<Node>& args)
{
Trace("pfee") << "pfee::assertFact " << lit << " " << id << ", exp = " << exp
<< ", args = " << args << std::endl;
Node atom = lit.getKind() == NOT ? lit[0] : lit;
bool polarity = lit.getKind() != NOT;
// register the step in the proof
if (holds(atom, polarity))
{
// we do not process this fact if it already holds
return false;
}
// must extract the explanation as a vector
std::vector<Node> expv;
// Flatten (single occurrences) of AND. We do not allow nested AND, it is
// the responsibilty of the caller to ensure these do not occur.
if (exp != d_true)
{
if (exp.getKind() == AND)
{
for (const Node& expc : exp)
{
// should not have doubly nested AND
Assert(expc.getKind() != AND);
expv.push_back(expc);
}
}
else
{
expv.push_back(exp);
}
}
// buffer the step in the fact proof generator
ProofStep ps;
ps.d_rule = id;
ps.d_children = expv;
ps.d_args = args;
d_factPg.addStep(lit, ps);
// add lazy step to proof
d_proof.addLazyStep(lit, &d_factPg);
// second, assert it to the equality engine
return assertFactInternal(atom, polarity, exp);
}
bool ProofEqEngine::assertFact(Node lit, Node exp, ProofStepBuffer& psb)
{
Trace("pfee") << "pfee::assertFact " << lit << ", exp = " << exp
<< " via buffer with " << psb.getNumSteps() << " steps"
<< std::endl;
Node atom = lit.getKind() == NOT ? lit[0] : lit;
bool polarity = lit.getKind() != NOT;
if (holds(atom, polarity))
{
// we do not process this fact if it already holds
return false;
}
// buffer the steps in the fact proof generator
const std::vector<std::pair<Node, ProofStep>>& steps = psb.getSteps();
for (const std::pair<Node, ProofStep>& step : steps)
{
d_factPg.addStep(step.first, step.second);
}
// add lazy step to proof
d_proof.addLazyStep(lit, &d_factPg);
// second, assert it to the equality engine
return assertFactInternal(atom, polarity, exp);
}
bool ProofEqEngine::assertFact(Node lit, Node exp, ProofGenerator* pg)
{
Trace("pfee") << "pfee::assertFact " << lit << ", exp = " << exp
<< " via generator" << std::endl;
Node atom = lit.getKind() == NOT ? lit[0] : lit;
bool polarity = lit.getKind() != NOT;
if (holds(atom, polarity))
{
// we do not process this fact if it already holds
return false;
}
// note the proof generator is responsible for remembering the explanation
d_proof.addLazyStep(lit, pg);
// second, assert it to the equality engine
return assertFactInternal(atom, polarity, exp);
}
TrustNode ProofEqEngine::assertConflict(Node lit)
{
Trace("pfee") << "pfee::assertConflict " << lit << std::endl;
std::vector<TNode> assumps;
explainWithProof(lit, assumps, &d_proof);
// lit may not be equivalent to false, but should rewrite to false
if (lit != d_false)
{
Assert(Rewriter::rewrite(lit) == d_false)
<< "pfee::assertConflict: conflict literal is not rewritable to "
"false";
std::vector<Node> exp;
exp.push_back(lit);
std::vector<Node> args;
if (!d_proof.addStep(d_false, PfRule::MACRO_SR_PRED_ELIM, exp, args))
{
Assert(false) << "pfee::assertConflict: failed conflict step";
return TrustNode::null();
}
}
return ensureProofForFact(
d_false, assumps, TrustNodeKind::CONFLICT, &d_proof);
}
TrustNode ProofEqEngine::assertConflict(PfRule id,
const std::vector<Node>& exp,
const std::vector<Node>& args)
{
Trace("pfee") << "pfee::assertConflict " << id << ", exp = " << exp
<< ", args = " << args << std::endl;
// conflict is same as lemma concluding false
return assertLemma(d_false, id, exp, {}, args);
}
TrustNode ProofEqEngine::assertConflict(const std::vector<Node>& exp,
ProofGenerator* pg)
{
Assert(pg != nullptr);
Trace("pfee") << "pfee::assertConflict " << exp << " via generator"
<< std::endl;
return assertLemma(d_false, exp, {}, pg);
}
TrustNode ProofEqEngine::assertLemma(Node conc,
PfRule id,
const std::vector<Node>& exp,
const std::vector<Node>& noExplain,
const std::vector<Node>& args)
{
Trace("pfee") << "pfee::assertLemma " << conc << " " << id
<< ", exp = " << exp << ", noExplain = " << noExplain
<< ", args = " << args << std::endl;
Assert(conc != d_true);
LazyCDProof tmpProof(d_pnm, &d_proof);
LazyCDProof* curr;
TrustNodeKind tnk;
// same policy as above: for conflicts, use existing lazy proof
if (conc == d_false)
{
curr = &d_proof;
tnk = TrustNodeKind::CONFLICT;
}
else
{
curr = &tmpProof;
tnk = TrustNodeKind::LEMMA;
}
// explain each literal in the vector
std::vector<TNode> assumps;
explainVecWithProof(tnk, assumps, exp, noExplain, curr);
// Register the proof step. We use a separate lazy CDProof which will make
// calls to curr above for the proofs of the literals in exp.
LazyCDProof outer(d_pnm, curr);
if (!outer.addStep(conc, id, exp, args))
{
// a step went wrong, e.g. during checking
Assert(false) << "pfee::assertConflict: register proof step";
return TrustNode::null();
}
// Now get the proof for conc.
return ensureProofForFact(conc, assumps, tnk, &outer);
}
TrustNode ProofEqEngine::assertLemma(Node conc,
const std::vector<Node>& exp,
const std::vector<Node>& noExplain,
ProofGenerator* pg)
{
Assert(pg != nullptr);
Trace("pfee") << "pfee::assertLemma " << conc << ", exp = " << exp
<< ", noExplain = " << noExplain << " via generator"
<< std::endl;
LazyCDProof tmpProof(d_pnm, &d_proof);
LazyCDProof* curr;
TrustNodeKind tnk;
// same policy as above: for conflicts, use existing lazy proof
if (conc == d_false)
{
curr = &d_proof;
tnk = TrustNodeKind::CONFLICT;
}
else
{
curr = &tmpProof;
tnk = TrustNodeKind::LEMMA;
}
// explain each literal in the vector
std::vector<TNode> assumps;
explainVecWithProof(tnk, assumps, exp, noExplain, curr);
// We use a lazy proof chain here. The provided proof generator sets up the
// "skeleton" that is the base of the proof we are constructing. The call to
// LazyCDProofChain::getProofFor will expand the leaves of this proof via
// calls to curr.
LazyCDProofChain outer(d_pnm, true, nullptr, curr, false);
outer.addLazyStep(conc, pg);
return ensureProofForFact(conc, assumps, tnk, &outer);
}
TrustNode ProofEqEngine::explain(Node conc)
{
Trace("pfee") << "pfee::explain " << conc << std::endl;
LazyCDProof tmpProof(d_pnm, &d_proof);
std::vector<TNode> assumps;
explainWithProof(conc, assumps, &tmpProof);
return ensureProofForFact(conc, assumps, TrustNodeKind::PROP_EXP, &tmpProof);
}
void ProofEqEngine::explainVecWithProof(TrustNodeKind& tnk,
std::vector<TNode>& assumps,
const std::vector<Node>& exp,
const std::vector<Node>& noExplain,
LazyCDProof* curr)
{
std::vector<Node> expn;
for (const Node& e : exp)
{
if (std::find(noExplain.begin(), noExplain.end(), e) == noExplain.end())
{
explainWithProof(e, assumps, curr);
}
else
{
// it did not have a proof; it was an assumption of the previous rule
assumps.push_back(e);
// it is not a conflict, since it may involve new literals
tnk = TrustNodeKind::LEMMA;
}
}
}
TrustNode ProofEqEngine::ensureProofForFact(Node conc,
const std::vector<TNode>& assumps,
TrustNodeKind tnk,
ProofGenerator* curr)
{
Trace("pfee-proof") << std::endl;
Trace("pfee-proof") << "pfee::ensureProofForFact: input " << conc << " via "
<< assumps << ", TrustNodeKind=" << tnk << std::endl;
NodeManager* nm = NodeManager::currentNM();
// The proof
std::shared_ptr<ProofNode> pf;
ProofGenerator* pfg = nullptr;
// the explanation is the conjunction of assumptions
Node exp;
// If proofs are enabled, generate the proof and possibly modify the
// assumptions to match SCOPE.
Assert(curr != nullptr);
Trace("pfee-proof") << "pfee::ensureProofForFact: make proof for fact"
<< std::endl;
// get the proof for conc
std::shared_ptr<ProofNode> pfBody = curr->getProofFor(conc);
if (pfBody == nullptr)
{
Trace("pfee-proof")
<< "pfee::ensureProofForFact: failed to make proof for fact"
<< std::endl
<< std::endl;
// should have existed
Assert(false) << "pfee::assertConflict: failed to get proof for " << conc;
return TrustNode::null();
}
// clone it so that we have a fresh copy
pfBody = d_pnm->clone(pfBody);
Trace("pfee-proof") << "pfee::ensureProofForFact: add scope" << std::endl;
// The free assumptions must be closed by assumps, which should be passed
// as arguments of SCOPE. However, some of the free assumptions may not
// literally be equal to assumps, for instance, due to symmetry. In other
// words, the SCOPE could be closing (= x y) in a proof with free
// assumption (= y x). We modify the proof leaves to account for this
// below.
std::vector<Node> scopeAssumps;
// we first ensure the assumptions are flattened
for (const TNode& a : assumps)
{
if (a.getKind() == AND)
{
scopeAssumps.insert(scopeAssumps.end(), a.begin(), a.end());
}
else
{
scopeAssumps.push_back(a);
}
}
// Scope the proof constructed above, and connect the formula with the proof
// minimize the assumptions.
pf = d_pnm->mkScope(pfBody, scopeAssumps, true, true);
// If we have no assumptions, and are proving an explanation for propagation
if (scopeAssumps.empty() && tnk == TrustNodeKind::PROP_EXP)
{
// Must add "true" as an explicit argument. This is to ensure that the
// propagation F from true proves (=> true F) instead of F, since this is
// the form required by TrustNodeKind::PROP_EXP. We do not ensure closed or
// minimize here, since we already ensured the proof was closed above, and
// we do not want to minimize, or else "true" would be omitted.
scopeAssumps.push_back(nm->mkConst(true));
pf = d_pnm->mkScope(pf, scopeAssumps, false);
}
exp = nm->mkAnd(scopeAssumps);
// Make the lemma or conflict node. This must exactly match the conclusion
// of SCOPE below.
Node formula;
if (tnk == TrustNodeKind::CONFLICT)
{
// conflict is negated
Assert(conc == d_false);
formula = exp;
}
else
{
formula =
exp == d_true
? conc
: (conc == d_false ? exp.negate() : nm->mkNode(IMPLIES, exp, conc));
}
Trace("pfee-proof") << "pfee::ensureProofForFact: formula is " << formula
<< std::endl;
// should always be non-null
Assert(pf != nullptr);
if (Trace.isOn("pfee-proof") || Trace.isOn("pfee-proof-final"))
{
Trace("pfee-proof") << "pfee::ensureProofForFact: printing proof"
<< std::endl;
std::stringstream ss;
pf->printDebug(ss);
Trace("pfee-proof") << "pfee::ensureProofForFact: Proof is " << ss.str()
<< std::endl;
}
// Should be a closed proof now. If it is not, then the overall proof
// is malformed.
Assert(pf->isClosed());
pfg = this;
// set the proof for the conflict or lemma, which can be queried later
switch (tnk)
{
case TrustNodeKind::CONFLICT: setProofForConflict(formula, pf); break;
case TrustNodeKind::LEMMA: setProofForLemma(formula, pf); break;
case TrustNodeKind::PROP_EXP: setProofForPropExp(conc, exp, pf); break;
default:
pfg = nullptr;
Unhandled() << "Unhandled trust node kind " << tnk;
break;
}
Trace("pfee-proof") << "pfee::ensureProofForFact: finish" << std::endl
<< std::endl;
// we can provide a proof for conflict, lemma or explained propagation
switch (tnk)
{
case TrustNodeKind::CONFLICT:
return TrustNode::mkTrustConflict(formula, pfg);
case TrustNodeKind::LEMMA: return TrustNode::mkTrustLemma(formula, pfg);
case TrustNodeKind::PROP_EXP:
return TrustNode::mkTrustPropExp(conc, exp, pfg);
default: Unhandled() << "Unhandled trust node kind " << tnk; break;
}
return TrustNode::null();
}
bool ProofEqEngine::assertFactInternal(TNode atom, bool polarity, TNode reason)
{
Trace("pfee-debug") << "pfee::assertFactInternal: " << atom << " " << polarity
<< " " << reason << std::endl;
bool ret;
if (atom.getKind() == EQUAL)
{
ret = d_ee.assertEquality(atom, polarity, reason);
}
else
{
ret = d_ee.assertPredicate(atom, polarity, reason);
}
if (ret)
{
// must reference count the new atom and explanation
d_keep.insert(atom);
d_keep.insert(reason);
}
return ret;
}
bool ProofEqEngine::holds(TNode atom, bool polarity)
{
if (atom.getKind() == EQUAL)
{
if (!d_ee.hasTerm(atom[0]) || !d_ee.hasTerm(atom[1]))
{
return false;
}
return polarity ? d_ee.areEqual(atom[0], atom[1])
: d_ee.areDisequal(atom[0], atom[1], false);
}
if (!d_ee.hasTerm(atom))
{
return false;
}
TNode b = polarity ? d_true : d_false;
return d_ee.areEqual(atom, b);
}
void ProofEqEngine::explainWithProof(Node lit,
std::vector<TNode>& assumps,
LazyCDProof* curr)
{
if (std::find(assumps.begin(), assumps.end(), lit) != assumps.end())
{
return;
}
std::shared_ptr<eq::EqProof> pf = std::make_shared<eq::EqProof>();
Trace("pfee-proof") << "pfee::explainWithProof: " << lit << std::endl;
bool polarity = lit.getKind() != NOT;
TNode atom = polarity ? lit : lit[0];
Assert(atom.getKind() != AND);
std::vector<TNode> tassumps;
if (atom.getKind() == EQUAL)
{
if (atom[0] == atom[1])
{
return;
}
Assert(d_ee.hasTerm(atom[0]));
Assert(d_ee.hasTerm(atom[1]));
if (!polarity)
{
// ensure the explanation exists
AlwaysAssert(d_ee.areDisequal(atom[0], atom[1], true));
}
d_ee.explainEquality(atom[0], atom[1], polarity, tassumps, pf.get());
}
else
{
Assert(d_ee.hasTerm(atom));
d_ee.explainPredicate(atom, polarity, tassumps, pf.get());
}
Trace("pfee-proof") << "...got " << tassumps << std::endl;
// avoid duplicates
for (TNode a : tassumps)
{
if (a == lit)
{
assumps.push_back(a);
}
else if (std::find(assumps.begin(), assumps.end(), a) == assumps.end())
{
assumps.push_back(a);
}
}
if (Trace.isOn("pfee-proof"))
{
Trace("pfee-proof") << "pfee::explainWithProof: add to proof ---"
<< std::endl;
std::stringstream sse;
pf->debug_print(sse);
Trace("pfee-proof") << sse.str() << std::endl;
Trace("pfee-proof") << "---" << std::endl;
}
// add the steps in the equality engine proof to the Proof
pf->addToProof(curr);
Trace("pfee-proof") << "pfee::explainWithProof: finished" << std::endl;
}
} // namespace eq
} // namespace theory
} // namespace cvc5
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