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/******************************************************************************
* Top contributors (to current version):
* Andrew Reynolds, Aina Niemetz
*
* 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.
* ****************************************************************************
*
* Alpha equivalence checking.
*/
#include "theory/quantifiers/alpha_equivalence.h"
#include "proof/method_id.h"
#include "proof/proof.h"
#include "proof/proof_node.h"
using namespace cvc5::kind;
namespace cvc5 {
namespace theory {
namespace quantifiers {
struct sortTypeOrder {
expr::TermCanonize* d_tu;
bool operator() (TypeNode i, TypeNode j) {
return d_tu->getIdForType( i )<d_tu->getIdForType( j );
}
};
Node AlphaEquivalenceTypeNode::registerNode(
Node q,
Node t,
std::vector<TypeNode>& typs,
std::map<TypeNode, size_t>& typCount)
{
AlphaEquivalenceTypeNode* aetn = this;
size_t index = 0;
while (index < typs.size())
{
TypeNode curr = typs[index];
Assert(typCount.find(curr) != typCount.end());
Trace("aeq-debug") << "[" << curr << " " << typCount[curr] << "] ";
std::pair<TypeNode, size_t> key(curr, typCount[curr]);
aetn = &(aetn->d_children[key]);
index = index + 1;
}
Trace("aeq-debug") << " : ";
std::map<Node, Node>::iterator it = aetn->d_quant.find(t);
if (it != aetn->d_quant.end())
{
return it->second;
}
aetn->d_quant[t] = q;
return q;
}
Node AlphaEquivalenceDb::addTerm(Node q)
{
Assert(q.getKind() == FORALL);
Trace("aeq") << "Alpha equivalence : register " << q << std::endl;
//construct canonical quantified formula
Node t = d_tc->getCanonicalTerm(q[1], d_sortCommutativeOpChildren);
Trace("aeq") << " canonical form: " << t << std::endl;
return addTermToTypeTrie(t, q);
}
Node AlphaEquivalenceDb::addTermWithSubstitution(Node q,
std::vector<Node>& vars,
std::vector<Node>& subs)
{
Trace("aeq") << "Alpha equivalence : register " << q << std::endl;
// construct canonical quantified formula with visited cache
std::map<TNode, Node> visited;
Node t = d_tc->getCanonicalTerm(q[1], visited, d_sortCommutativeOpChildren);
// only need to store BOUND_VARIABLE in substitution
std::map<Node, TNode>& bm = d_bvmap[q];
for (const std::pair<const TNode, Node>& b : visited)
{
if (b.first.getKind() == BOUND_VARIABLE)
{
Assert(b.second.getKind() == BOUND_VARIABLE);
bm[b.second] = b.first;
}
}
Node qret = addTermToTypeTrie(t, q);
if (qret != q)
{
Assert(d_bvmap.find(qret) != d_bvmap.end());
std::map<Node, TNode>& bmr = d_bvmap[qret];
std::map<Node, TNode>::iterator itb;
for (const std::pair<const Node, TNode>& b : bmr)
{
itb = bm.find(b.first);
if (itb == bm.end())
{
// didn't use the same variables, fail
vars.clear();
subs.clear();
break;
}
// otherwise, we map the variable in the returned quantified formula
// to the variable that used the same canonical variable
vars.push_back(b.second);
subs.push_back(itb->second);
}
}
return qret;
}
Node AlphaEquivalenceDb::addTermToTypeTrie(Node t, Node q)
{
//compute variable type counts
std::map<TypeNode, size_t> typCount;
std::vector< TypeNode > typs;
for (const Node& v : q[0])
{
TypeNode tn = v.getType();
typCount[tn]++;
if( std::find( typs.begin(), typs.end(), tn )==typs.end() ){
typs.push_back( tn );
}
}
sortTypeOrder sto;
sto.d_tu = d_tc;
std::sort( typs.begin(), typs.end(), sto );
Trace("aeq-debug") << " ";
Node ret = d_ae_typ_trie.registerNode(q, t, typs, typCount);
Trace("aeq") << " ...result : " << ret << std::endl;
return ret;
}
AlphaEquivalence::AlphaEquivalence(Env& env)
: EnvObj(env),
d_termCanon(),
d_aedb(&d_termCanon, true),
d_pnm(env.getProofNodeManager()),
d_pfAlpha(d_pnm ? new EagerProofGenerator(d_pnm) : nullptr)
{
}
TrustNode AlphaEquivalence::reduceQuantifier(Node q)
{
Assert(q.getKind() == FORALL);
Node ret;
std::vector<Node> vars;
std::vector<Node> subs;
if (isProofEnabled())
{
ret = d_aedb.addTermWithSubstitution(q, vars, subs);
}
else
{
ret = d_aedb.addTerm(q);
}
if (ret == q)
{
return TrustNode::null();
}
Node lem;
ProofGenerator* pg = nullptr;
// lemma ( q <=> d_quant )
// Notice that we infer this equivalence regardless of whether q or ret
// have annotations (e.g. user patterns, names, etc.).
Trace("alpha-eq") << "Alpha equivalent : " << std::endl;
Trace("alpha-eq") << " " << q << std::endl;
Trace("alpha-eq") << " " << ret << std::endl;
lem = ret.eqNode(q);
if (q.getNumChildren() == 3)
{
verbose(1) << "Ignoring annotated quantified formula based on alpha "
"equivalence: "
<< q << std::endl;
}
// if successfully computed the substitution above
if (isProofEnabled() && !vars.empty())
{
std::vector<Node> pfArgs;
pfArgs.push_back(ret);
for (size_t i = 0, nvars = vars.size(); i < nvars; i++)
{
pfArgs.push_back(vars[i].eqNode(subs[i]));
Trace("alpha-eq") << "subs: " << vars[i] << " -> " << subs[i]
<< std::endl;
}
CDProof cdp(d_pnm);
Node sret =
ret.substitute(vars.begin(), vars.end(), subs.begin(), subs.end());
std::vector<Node> transEq;
Node eq = ret.eqNode(sret);
transEq.push_back(eq);
// ---------- ALPHA_EQUIV
// ret = sret
cdp.addStep(eq, PfRule::ALPHA_EQUIV, {}, pfArgs);
// if not syntactically equal, maybe it can be transformed
bool success = false;
if (sret == q)
{
success = true;
}
else
{
Node eq2 = sret.eqNode(q);
transEq.push_back(eq2);
Node eq2r = extendedRewrite(eq2);
if (eq2r.isConst() && eq2r.getConst<bool>())
{
// ---------- MACRO_SR_PRED_INTRO
// sret = q
std::vector<Node> pfArgs2;
pfArgs2.push_back(eq2);
addMethodIds(pfArgs2,
MethodId::SB_DEFAULT,
MethodId::SBA_SEQUENTIAL,
MethodId::RW_EXT_REWRITE);
cdp.addStep(eq2, PfRule::MACRO_SR_PRED_INTRO, {}, pfArgs2);
success = true;
}
}
// if successful, store the proof and remember the proof generator
if (success)
{
if (transEq.size() > 1)
{
// TRANS of ALPHA_EQ and MACRO_SR_PRED_INTRO steps from above
cdp.addStep(lem, PfRule::TRANS, transEq, {});
}
std::shared_ptr<ProofNode> pn = cdp.getProofFor(lem);
Trace("alpha-eq") << "Proof is " << *pn.get() << std::endl;
d_pfAlpha->setProofFor(lem, pn);
pg = d_pfAlpha.get();
}
}
return TrustNode::mkTrustLemma(lem, pg);
}
bool AlphaEquivalence::isProofEnabled() const { return d_pfAlpha != nullptr; }
} // namespace quantifiers
} // namespace theory
} // namespace cvc5
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