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GCC Code Coverage Report
Directory:	.		Exec	Total	Coverage
File:	src/theory/quantifiers/sygus/synth_conjecture.cpp	Lines:	525	590	89.0 %
Date:	2021-09-30	Branches:	1067	2592	41.2 %

/******************************************************************************
 * Top contributors (to current version):
 *   Andrew Reynolds, Mathias Preiner, Haniel Barbosa
 *
 * 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.
 * ****************************************************************************
 *
 * Implementation of class that encapsulates techniques for a single
 * (SyGuS) synthesis conjecture.
 */
#include "theory/quantifiers/sygus/synth_conjecture.h"

#include "base/configuration.h"
#include "expr/node_algorithm.h"
#include "expr/skolem_manager.h"
#include "options/base_options.h"
#include "options/datatypes_options.h"
#include "options/quantifiers_options.h"
#include "printer/printer.h"
#include "smt/logic_exception.h"
#include "smt/smt_statistics_registry.h"
#include "theory/datatypes/sygus_datatype_utils.h"
#include "theory/quantifiers/first_order_model.h"
#include "theory/quantifiers/instantiate.h"
#include "theory/quantifiers/quantifiers_attributes.h"
#include "theory/quantifiers/sygus/enum_value_manager.h"
#include "theory/quantifiers/sygus/sygus_grammar_cons.h"
#include "theory/quantifiers/sygus/sygus_pbe.h"
#include "theory/quantifiers/sygus/synth_engine.h"
#include "theory/quantifiers/sygus/term_database_sygus.h"
#include "theory/quantifiers/term_util.h"
#include "theory/rewriter.h"
#include "theory/smt_engine_subsolver.h"

using namespace cvc5::kind;
using namespace std;

namespace cvc5 {
namespace theory {
namespace quantifiers {

SynthConjecture::SynthConjecture(Env& env,
                                 QuantifiersState& qs,
                                 QuantifiersInferenceManager& qim,
                                 QuantifiersRegistry& qr,
                                 TermRegistry& tr,
                                 SygusStatistics& s)
    : EnvObj(env),
      d_qstate(qs),
      d_qim(qim),
      d_qreg(qr),
      d_treg(tr),
      d_stats(s),
      d_tds(tr.getTermDatabaseSygus()),
      d_verify(options(), qs.getLogicInfo(), d_tds),
      d_hasSolution(false),
      d_ceg_si(new CegSingleInv(env, tr, s)),
      d_templInfer(new SygusTemplateInfer),
      d_ceg_proc(new SynthConjectureProcess),
      d_ceg_gc(new CegGrammarConstructor(d_tds, this)),
      d_sygus_rconst(new SygusRepairConst(env, d_tds)),
      d_exampleInfer(new ExampleInfer(d_tds)),
      d_ceg_pbe(new SygusPbe(env, qs, qim, d_tds, this)),
      d_ceg_cegis(new Cegis(env, qs, qim, d_tds, this)),
      d_ceg_cegisUnif(new CegisUnif(env, qs, qim, d_tds, this)),
      d_sygus_ccore(new CegisCoreConnective(env, qs, qim, d_tds, this)),
      d_master(nullptr),
      d_set_ce_sk_vars(false),
      d_repair_index(0),
      d_guarded_stream_exc(false)
{
  if (options::sygusSymBreakPbe() || options::sygusUnifPbe())
  {
    d_modules.push_back(d_ceg_pbe.get());
  }
  if (options::sygusUnifPi() != options::SygusUnifPiMode::NONE)
  {
    d_modules.push_back(d_ceg_cegisUnif.get());
  }
  if (options::sygusCoreConnective())
  {
    d_modules.push_back(d_sygus_ccore.get());
  }
  d_modules.push_back(d_ceg_cegis.get());
}

SynthConjecture::~SynthConjecture() {}

void SynthConjecture::presolve()
{
  // we don't have a solution yet
  d_hasSolution = false;
}

void SynthConjecture::assign(Node q)
{
  Assert(d_embed_quant.isNull());
  Assert(q.getKind() == FORALL);
  Trace("cegqi") << "SynthConjecture : assign : " << q << std::endl;
  d_quant = q;
  NodeManager* nm = NodeManager::currentNM();
  SkolemManager* sm = nm->getSkolemManager();

  // initialize the guard
  d_feasible_guard = sm->mkDummySkolem("G", nm->booleanType());
  d_feasible_guard = Rewriter::rewrite(d_feasible_guard);
  d_feasible_guard = d_qstate.getValuation().ensureLiteral(d_feasible_guard);
  AlwaysAssert(!d_feasible_guard.isNull());

  // pre-simplify the quantified formula based on the process utility
  d_simp_quant = d_ceg_proc->preSimplify(d_quant);

  // compute its attributes
  QAttributes qa;
  QuantAttributes::computeQuantAttributes(q, qa);

  std::map<Node, Node> templates;
  std::map<Node, Node> templates_arg;
  // register with single invocation if applicable
  if (qa.d_sygus)
  {
    d_ceg_si->initialize(d_simp_quant);
    d_simp_quant = d_ceg_si->getSimplifiedConjecture();
    if (!d_ceg_si->isSingleInvocation())
    {
      d_templInfer->initialize(d_simp_quant);
    }
    // carry the templates
    for (const Node& v : q[0])
    {
      Node templ = d_templInfer->getTemplate(v);
      if (!templ.isNull())
      {
        templates[v] = templ;
        templates_arg[v] = d_templInfer->getTemplateArg(v);
      }
    }
  }

  // post-simplify the quantified formula based on the process utility
  d_simp_quant = d_ceg_proc->postSimplify(d_simp_quant);

  // finished simplifying the quantified formula at this point

  // convert to deep embedding and finalize single invocation here
  d_embed_quant = d_ceg_gc->process(d_simp_quant, templates, templates_arg);
  Trace("cegqi") << "SynthConjecture : converted to embedding : "
                 << d_embed_quant << std::endl;

  Node sc = qa.d_sygusSideCondition;
  if (!sc.isNull())
  {
    // convert to deep embedding
    d_embedSideCondition = d_ceg_gc->convertToEmbedding(sc);
    Trace("cegqi") << "SynthConjecture : side condition : "
                   << d_embedSideCondition << std::endl;
  }

  // we now finalize the single invocation module, based on the syntax
  // restrictions
  if (qa.d_sygus)
  {
    d_ceg_si->finishInit(d_ceg_gc->isSyntaxRestricted());
  }

  Assert(d_candidates.empty());
  std::vector<Node> vars;
  for (unsigned i = 0; i < d_embed_quant[0].getNumChildren(); i++)
  {
    vars.push_back(d_embed_quant[0][i]);
    Node e = sm->mkDummySkolem("e", d_embed_quant[0][i].getType());
    d_candidates.push_back(e);
  }
  Trace("cegqi") << "Base quantified formula is : " << d_embed_quant
                 << std::endl;
  // construct base instantiation
  d_base_inst = Rewriter::rewrite(d_qim.getInstantiate()->getInstantiation(
      d_embed_quant, vars, d_candidates));
  if (!d_embedSideCondition.isNull() && !vars.empty())
  {
    d_embedSideCondition = d_embedSideCondition.substitute(
        vars.begin(), vars.end(), d_candidates.begin(), d_candidates.end());
  }
  Trace("cegqi") << "Base instantiation is :      " << d_base_inst << std::endl;

  // initialize the sygus constant repair utility
  if (options::sygusRepairConst())
  {
    d_sygus_rconst->initialize(d_base_inst.negate(), d_candidates);
    if (options::sygusConstRepairAbort())
    {
      if (!d_sygus_rconst->isActive())
      {
        // no constant repair is possible: abort
        std::stringstream ss;
        ss << "Grammar does not allow repair constants." << std::endl;
        throw LogicException(ss.str());
      }
    }
  }
  // initialize the example inference utility
  // Notice that we must also consider the side condition when inferring
  // whether the conjecture is PBE. This ensures we do not prune solutions
  // that may satisfy the side condition based on equivalence-up-to-examples
  // with solutions that do not.
  Node conjForExamples = d_base_inst;
  if (!d_embedSideCondition.isNull())
  {
    conjForExamples = nm->mkNode(AND, d_embedSideCondition, d_base_inst);
  }
  if (d_exampleInfer!=nullptr && !d_exampleInfer->initialize(conjForExamples, d_candidates))
  {
    // there is a contradictory example pair, the conjecture is infeasible.
    Node infLem = d_feasible_guard.negate();
    d_qim.lemma(infLem, InferenceId::QUANTIFIERS_SYGUS_EXAMPLE_INFER_CONTRA);
    // we don't need to continue initialization in this case
    return;
  }

  // register this term with sygus database and other utilities that impact
  // the enumerative sygus search
  if (!isSingleInvocation())
  {
    d_ceg_proc->initialize(d_base_inst, d_candidates);
    for (unsigned i = 0, size = d_modules.size(); i < size; i++)
    {
      if (d_modules[i]->initialize(d_simp_quant, d_base_inst, d_candidates))
      {
        d_master = d_modules[i];
        break;
      }
    }
    Assert(d_master != nullptr);
  }

  Assert(d_qreg.getQuantAttributes().isSygus(q));
  // if the base instantiation is an existential, store its variables
  if (d_base_inst.getKind() == NOT && d_base_inst[0].getKind() == FORALL)
  {
    for (const Node& v : d_base_inst[0][0])
    {
      d_inner_vars.push_back(v);
    }
  }

  // register the strategy
  d_feasible_strategy.reset(new DecisionStrategySingleton(
      d_env, "sygus_feasible", d_feasible_guard, d_qstate.getValuation()));
  d_qim.getDecisionManager()->registerStrategy(
      DecisionManager::STRAT_QUANT_SYGUS_FEASIBLE, d_feasible_strategy.get());
  // this must be called, both to ensure that the feasible guard is
  // decided on with true polariy, but also to ensure that output channel
  // has been used on this call to check.
  d_qim.requirePhase(d_feasible_guard, true);

  Trace("cegqi") << "...finished, single invocation = " << isSingleInvocation()
                 << std::endl;
}

Node SynthConjecture::getGuard() const { return d_feasible_guard; }

bool SynthConjecture::isSingleInvocation() const
{
  return d_ceg_si->isSingleInvocation();
}

bool SynthConjecture::needsCheck()
{
  bool value;
  Assert(!d_feasible_guard.isNull());
  // non or fully single invocation : look at guard only
  if (d_qstate.getValuation().hasSatValue(d_feasible_guard, value))
  {
    if (!value)
    {
      Trace("sygus-engine-debug") << "Conjecture is infeasible." << std::endl;
      Warning() << "Warning : the SyGuS conjecture may be infeasible"
                << std::endl;
      return false;
    }
    else
    {
      Trace("sygus-engine-debug") << "Feasible guard " << d_feasible_guard
                                  << " assigned true." << std::endl;
    }
  }
  else
  {
    Trace("cegqi-warn") << "WARNING: Guard " << d_feasible_guard
                        << " is not assigned!" << std::endl;
    Assert(false);
  }
  return true;
}

bool SynthConjecture::needsRefinement() const { return d_set_ce_sk_vars; }
bool SynthConjecture::doCheck()
{
  if (isSingleInvocation())
  {
    // We now try to solve with the single invocation solver, which may or may
    // not succeed in solving the conjecture. In either case,  we are done and
    // return true.
    if (d_ceg_si->solve())
    {
      d_hasSolution = true;
      // the conjecture has a solution, so its negation holds
      Node qn = d_quant.negate();
      d_qim.addPendingLemma(qn, InferenceId::QUANTIFIERS_SYGUS_SI_SOLVED);
    }
    return true;
  }
  Assert(d_master != nullptr);
  Assert(!d_hasSolution);

  // get the list of terms that the master strategy is interested in
  std::vector<Node> terms;
  d_master->getTermList(d_candidates, terms);

  Assert(!d_candidates.empty());

  Trace("cegqi-check") << "CegConjuncture : check, build candidates..."
                       << std::endl;
  std::vector<Node> candidate_values;
  bool constructed_cand = false;

  // If a module is not trying to repair constants in solutions and the option
  // sygusRepairConst  is true, we use a default scheme for trying to repair
  // constants here.
  bool doRepairConst =
      options::sygusRepairConst() && !d_master->usingRepairConst();
  if (doRepairConst)
  {
    // have we tried to repair the previous solution?
    // if not, call the repair constant utility
    unsigned ninst = d_cinfo[d_candidates[0]].d_inst.size();
    if (d_repair_index < ninst)
    {
      std::vector<Node> fail_cvs;
      for (const Node& cprog : d_candidates)
      {
        Assert(d_repair_index < d_cinfo[cprog].d_inst.size());
        fail_cvs.push_back(d_cinfo[cprog].d_inst[d_repair_index]);
      }
      if (Trace.isOn("sygus-engine"))
      {
        Trace("sygus-engine") << "CegConjuncture : repair previous solution ";
        for (const Node& fc : fail_cvs)
        {
          std::stringstream ss;
          TermDbSygus::toStreamSygus(ss, fc);
          Trace("sygus-engine") << ss.str() << " ";
        }
        Trace("sygus-engine") << std::endl;
      }
      d_repair_index++;
      if (d_sygus_rconst->repairSolution(
              d_candidates, fail_cvs, candidate_values, true))
      {
        constructed_cand = true;
      }
    }
  }

  bool printDebug = d_env.isOutputOn(options::OutputTag::SYGUS);
  if (!constructed_cand)
  {
    // get the model value of the relevant terms from the master module
    std::vector<Node> enum_values;
    bool activeIncomplete = false;
    bool fullModel = getEnumeratedValues(terms, enum_values, activeIncomplete);

    // if the master requires a full model and the model is partial, we fail
    if (!d_master->allowPartialModel() && !fullModel)
    {
      // we retain the values in d_ev_active_gen_waiting
      Trace("sygus-engine-debug") << "...partial model, fail." << std::endl;
      // if we are partial due to an active enumerator, we may still succeed
      // on the next call
      return !activeIncomplete;
    }
    // determine if we had at least one value for an enumerator
    Assert(terms.size() == enum_values.size());
    bool modelSuccess = false;
    for (unsigned i = 0, size = terms.size(); i < size; i++)
    {
      if (!enum_values[i].isNull())
      {
        modelSuccess = true;
      }
    }
    if (modelSuccess)
    {
      // Must separately compute whether trace is on due to compilation of
      // Trace.isOn.
      bool traceIsOn = Trace.isOn("sygus-engine");
      if (printDebug || traceIsOn)
      {
        Trace("sygus-engine") << "  * Value is : ";
        std::stringstream sygusEnumOut;
        FirstOrderModel* m = d_treg.getModel();
        for (unsigned i = 0, size = terms.size(); i < size; i++)
        {
          Node nv = enum_values[i];
          Node onv = nv.isNull() ? m->getValue(terms[i]) : nv;
          TypeNode tn = onv.getType();
          std::stringstream ss;
          TermDbSygus::toStreamSygus(ss, onv);
          if (printDebug)
          {
            sygusEnumOut << " " << ss.str();
          }
          Trace("sygus-engine") << terms[i] << " -> ";
          if (nv.isNull())
          {
            Trace("sygus-engine") << "[EXC: " << ss.str() << "] ";
          }
          else
          {
            Trace("sygus-engine") << ss.str() << " ";
            if (Trace.isOn("sygus-engine-rr"))
            {
              Node bv = d_tds->sygusToBuiltin(nv, tn);
              bv = Rewriter::rewrite(bv);
              Trace("sygus-engine-rr") << " -> " << bv << std::endl;
            }
          }
        }
        Trace("sygus-engine") << std::endl;
        if (d_env.isOutputOn(options::OutputTag::SYGUS))
        {
          d_env.getOutput(options::OutputTag::SYGUS)
              << "(sygus-enum" << sygusEnumOut.str() << ")" << std::endl;
        }
      }
      Assert(candidate_values.empty());
      constructed_cand = d_master->constructCandidates(
          terms, enum_values, d_candidates, candidate_values);
    }
    // notify the enumerator managers of the status of the candidate
    for (std::pair<const Node, std::unique_ptr<EnumValueManager>>& ecp :
         d_enumManager)
    {
      ecp.second->notifyCandidate(modelSuccess);
    }
    // if we did not generate a candidate, return now
    if (!modelSuccess)
    {
      Trace("sygus-engine-debug") << "...empty model, fail." << std::endl;
      return !activeIncomplete;
    }
  }

  NodeManager* nm = NodeManager::currentNM();
  SkolemManager* sm = nm->getSkolemManager();

  // check the side condition if we constructed a candidate
  if (constructed_cand)
  {
    if (!checkSideCondition(candidate_values))
    {
      excludeCurrentSolution(terms, candidate_values);
      Trace("sygus-engine") << "...failed side condition" << std::endl;
      return false;
    }
  }

  // must get a counterexample to the value of the current candidate
  Node inst;
  if (constructed_cand)
  {
    if (Trace.isOn("cegqi-check"))
    {
      Trace("cegqi-check") << "CegConjuncture : check candidate : "
                           << std::endl;
      for (unsigned i = 0, size = candidate_values.size(); i < size; i++)
      {
        Trace("cegqi-check") << "  " << i << " : " << d_candidates[i] << " -> "
                             << candidate_values[i] << std::endl;
      }
    }
    Assert(candidate_values.size() == d_candidates.size());
    inst = d_base_inst.substitute(d_candidates.begin(),
                                  d_candidates.end(),
                                  candidate_values.begin(),
                                  candidate_values.end());
  }
  else
  {
    inst = d_base_inst;
  }

  if (!constructed_cand)
  {
    return false;
  }

  // if we trust the sampling we ran, we terminate now
  if (options::cegisSample() == options::CegisSampleMode::TRUST)
  {
    // we have that the current candidate passed a sample test
    // since we trust sampling in this mode, we assert there is no
    // counterexample to the conjecture here.
    Node qn = d_quant.negate();
    d_qim.addPendingLemma(qn,
                          InferenceId::QUANTIFIERS_SYGUS_SAMPLE_TRUST_SOLVED);
    recordSolution(candidate_values);
    return true;
  }
  Assert(!d_set_ce_sk_vars);

  // immediately skolemize inner existentials
  Node query;
  // introduce the skolem variables
  std::vector<Node> sks;
  std::vector<Node> vars;
  if (constructed_cand)
  {
    if (printDebug)
    {
      const Options& sopts = options();
      std::ostream& out = *sopts.base.out;
      out << "(sygus-candidate ";
      Assert(d_quant[0].getNumChildren() == candidate_values.size());
      for (unsigned i = 0, ncands = candidate_values.size(); i < ncands; i++)
      {
        Node v = candidate_values[i];
        std::stringstream ss;
        TermDbSygus::toStreamSygus(ss, v);
        out << "(" << d_quant[0][i] << " " << ss.str() << ")";
      }
      out << ")" << std::endl;
    }
    if (inst.getKind() == NOT && inst[0].getKind() == FORALL)
    {
      for (const Node& v : inst[0][0])
      {
        Node sk = sm->mkDummySkolem("rsk", v.getType());
        sks.push_back(sk);
        vars.push_back(v);
        Trace("cegqi-check-debug")
            << "  introduce skolem " << sk << " for " << v << "\n";
      }
      query = inst[0][1].substitute(
          vars.begin(), vars.end(), sks.begin(), sks.end());
      query = query.negate();
    }
    else
    {
      // use the instance itself
      query = inst;
    }
  }
  d_ce_sk_vars.insert(d_ce_sk_vars.end(), sks.begin(), sks.end());
  d_set_ce_sk_vars = true;

  if (query.isNull())
  {
    // no lemma to check
    return false;
  }

  // Record the solution, which may be falsified below. We require recording
  // here since the result of the satisfiability test may be unknown.
  recordSolution(candidate_values);

  Result r = d_verify.verify(query, d_ce_sk_vars, d_ce_sk_var_mvs);

  if (r.asSatisfiabilityResult().isSat() == Result::SAT)
  {
    // we have a counterexample
    return false;
  }
  else if (r.asSatisfiabilityResult().isSat() != Result::UNSAT)
  {
    // In the rare case that the subcall is unknown, we simply exclude the
    // solution, without adding a counterexample point. This should only
    // happen if the quantifier free logic is undecidable.
    excludeCurrentSolution(terms, candidate_values);
    // We should set incomplete, since a "sat" answer should not be
    // interpreted as "infeasible", which would make a difference in the rare
    // case where e.g. we had a finite grammar and exhausted the grammar.
    d_qim.setIncomplete(IncompleteId::QUANTIFIERS_SYGUS_NO_VERIFY);
    return false;
  }
  // otherwise we are unsat, and we will process the solution below

  // now mark that we have a solution
  d_hasSolution = true;
  if (options::sygusStream())
  {
    // immediately print the current solution
    printAndContinueStream(terms, candidate_values);
    // streaming means now we immediately are looking for a new solution
    d_hasSolution = false;
    return false;
  }
  // Use lemma to terminate with "unsat", this is justified by the verification
  // check above, which confirms the synthesis conjecture is solved.
  Node qn = d_quant.negate();
  d_qim.addPendingLemma(qn, InferenceId::QUANTIFIERS_SYGUS_VERIFY_SOLVED);
  return true;
}

bool SynthConjecture::checkSideCondition(const std::vector<Node>& cvals) const
{
  if (!d_embedSideCondition.isNull())
  {
    Node sc = d_embedSideCondition;
    if (!cvals.empty())
    {
      sc = sc.substitute(
        d_candidates.begin(), d_candidates.end(), cvals.begin(), cvals.end());
    }
    Trace("sygus-engine") << "Check side condition..." << std::endl;
    Trace("cegqi-debug") << "Check side condition : " << sc << std::endl;
    Result r = checkWithSubsolver(sc, options(), logicInfo());
    Trace("cegqi-debug") << "...got side condition : " << r << std::endl;
    if (r == Result::UNSAT)
    {
      return false;
    }
    Trace("sygus-engine") << "...passed side condition" << std::endl;
  }
  return true;
}

bool SynthConjecture::doRefine()
{
  Assert(d_set_ce_sk_vars);

  // first, make skolem substitution
  Trace("cegqi-refine") << "doRefine : construct skolem substitution..."
                        << std::endl;
  std::vector<Node> sk_vars;
  std::vector<Node> sk_subs;
  // collect the substitution over all disjuncts
  if (!d_ce_sk_vars.empty())
  {
    Trace("cegqi-refine") << "Get model values for skolems..." << std::endl;
    Assert(d_inner_vars.size() == d_ce_sk_vars.size());
    if (d_ce_sk_var_mvs.empty())
    {
      std::vector<Node> model_values;
      for (const Node& v : d_ce_sk_vars)
      {
        Node mv = getModelValue(v);
        Trace("cegqi-refine") << "  " << v << " -> " << mv << std::endl;
        model_values.push_back(mv);
      }
      sk_subs.insert(sk_subs.end(), model_values.begin(), model_values.end());
    }
    else
    {
      Assert(d_ce_sk_var_mvs.size() == d_ce_sk_vars.size());
      sk_subs.insert(
          sk_subs.end(), d_ce_sk_var_mvs.begin(), d_ce_sk_var_mvs.end());
    }
    sk_vars.insert(sk_vars.end(), d_inner_vars.begin(), d_inner_vars.end());
  }
  else
  {
    Assert(d_inner_vars.empty());
  }

  Trace("cegqi-refine") << "doRefine : Construct refinement lemma..."
                        << std::endl;
  Trace("cegqi-refine-debug")
      << "  For counterexample skolems : " << d_ce_sk_vars << std::endl;
  Node base_lem;
  if (d_base_inst.getKind() == NOT && d_base_inst[0].getKind() == FORALL)
  {
    base_lem = d_base_inst[0][1];
  }
  else
  {
    base_lem = d_base_inst.negate();
  }

  Assert(sk_vars.size() == sk_subs.size());

  Trace("cegqi-refine") << "doRefine : substitute..." << std::endl;
  base_lem = base_lem.substitute(
      sk_vars.begin(), sk_vars.end(), sk_subs.begin(), sk_subs.end());
  Trace("cegqi-refine") << "doRefine : rewrite..." << std::endl;
  base_lem = d_tds->rewriteNode(base_lem);
  Trace("cegqi-refine") << "doRefine : register refinement lemma " << base_lem
                        << "..." << std::endl;
  size_t prevPending = d_qim.numPendingLemmas();
  d_master->registerRefinementLemma(sk_vars, base_lem);
  Trace("cegqi-refine") << "doRefine : finished" << std::endl;
  d_set_ce_sk_vars = false;
  d_ce_sk_vars.clear();
  d_ce_sk_var_mvs.clear();

  // check if we added a lemma
  bool addedLemma = d_qim.numPendingLemmas() > prevPending;
  if (addedLemma)
  {
    Trace("sygus-engine-debug") << "  ...refine candidate." << std::endl;
  }
  else
  {
    Trace("sygus-engine-debug") << "  ...(warning) failed to refine candidate, "
                                   "manually exclude candidate."
                                << std::endl;
    std::vector<Node> cvals;
    for (const Node& c : d_candidates)
    {
      cvals.push_back(d_cinfo[c].d_inst.back());
    }
    // something went wrong, exclude the current candidate
    excludeCurrentSolution(d_candidates, cvals);
    // Note this happens when evaluation is incapable of disproving a candidate
    // for counterexample point c, but satisfiability checking happened to find
    // the the same point c is indeed a true counterexample. It is sound
    // to exclude the candidate in this case.
  }
  return addedLemma;
}

void SynthConjecture::preregisterConjecture(Node q)
{
  d_ceg_si->preregisterConjecture(q);
}

bool SynthConjecture::getEnumeratedValues(std::vector<Node>& n,
                                          std::vector<Node>& v,
                                          bool& activeIncomplete)
{
  std::vector<Node> ncheck = n;
  n.clear();
  bool ret = true;
  for (unsigned i = 0, size = ncheck.size(); i < size; i++)
  {
    Node e = ncheck[i];
    // if it is not active, we return null
    Node g = d_tds->getActiveGuardForEnumerator(e);
    if (!g.isNull())
    {
      Node gstatus = d_qstate.getValuation().getSatValue(g);
      if (gstatus.isNull() || !gstatus.getConst<bool>())
      {
        Trace("sygus-engine-debug")
            << "Enumerator " << e << " is inactive." << std::endl;
        continue;
      }
    }
    EnumValueManager* eman = getEnumValueManagerFor(e);
    Node nv = eman->getEnumeratedValue(activeIncomplete);
    n.push_back(e);
    v.push_back(nv);
    ret = ret && !nv.isNull();
  }
  return ret;
}

EnumValueManager* SynthConjecture::getEnumValueManagerFor(Node e)
{
  std::map<Node, std::unique_ptr<EnumValueManager>>::iterator it =
      d_enumManager.find(e);
  if (it != d_enumManager.end())
  {
    return it->second.get();
  }
  // otherwise, allocate it
  Node f = d_tds->getSynthFunForEnumerator(e);
  bool hasExamples = (d_exampleInfer != nullptr && d_exampleInfer->hasExamples(f)
                      && d_exampleInfer->getNumExamples(f) != 0);
  d_enumManager[e].reset(new EnumValueManager(
      d_env, d_qstate, d_qim, d_treg, d_stats, e, hasExamples));
  EnumValueManager* eman = d_enumManager[e].get();
  // set up the examples
  if (hasExamples)
  {
    ExampleEvalCache* eec = eman->getExampleEvalCache();
    Assert(eec != nullptr);
    for (unsigned i = 0, nex = d_exampleInfer->getNumExamples(f); i < nex; i++)
    {
      std::vector<Node> input;
      d_exampleInfer->getExample(f, i, input);
      eec->addExample(input);
    }
  }
  return eman;
}

Node SynthConjecture::getModelValue(Node n)
{
  Trace("cegqi-mv") << "getModelValue for : " << n << std::endl;
  return d_treg.getModel()->getValue(n);
}

void SynthConjecture::debugPrint(const char* c)
{
  Trace(c) << "Synthesis conjecture : " << d_embed_quant << std::endl;
  Trace(c) << "  * Candidate programs : " << d_candidates << std::endl;
  Trace(c) << "  * Counterexample skolems : " << d_ce_sk_vars << std::endl;
}

void SynthConjecture::printAndContinueStream(const std::vector<Node>& enums,
                                             const std::vector<Node>& values)
{
  Assert(d_master != nullptr);
  // we have generated a solution, print it
  // get the current output stream
  printSynthSolutionInternal(*options().base.out);
  excludeCurrentSolution(enums, values);
}

void SynthConjecture::excludeCurrentSolution(const std::vector<Node>& enums,
                                             const std::vector<Node>& values)
{
  Trace("cegqi-debug") << "Exclude current solution: " << enums << " / "
                       << values << std::endl;
  // We will not refine the current candidate solution since it is a solution
  // thus, we clear information regarding the current refinement
  d_set_ce_sk_vars = false;
  d_ce_sk_vars.clear();
  d_ce_sk_var_mvs.clear();
  // However, we need to exclude the current solution using an explicit
  // blocking clause, so that we proceed to the next solution. We do this only
  // for passively-generated enumerators (TermDbSygus::isPassiveEnumerator).
  std::vector<Node> exp;
  for (unsigned i = 0, tsize = enums.size(); i < tsize; i++)
  {
    Node cprog = enums[i];
    Assert(d_tds->isEnumerator(cprog));
    if (d_tds->isPassiveEnumerator(cprog))
    {
      Node cval = values[i];
      // add to explanation of exclusion
      d_tds->getExplain()->getExplanationForEquality(cprog, cval, exp);
    }
  }
  if (!exp.empty())
  {
    if (!d_guarded_stream_exc)
    {
      d_guarded_stream_exc = true;
      exp.push_back(d_feasible_guard);
    }
    Node exc_lem = exp.size() == 1
                       ? exp[0]
                       : NodeManager::currentNM()->mkNode(kind::AND, exp);
    exc_lem = exc_lem.negate();
    Trace("cegqi-lemma") << "Cegqi::Lemma : stream exclude current solution : "
                         << exc_lem << std::endl;
    d_qim.lemma(exc_lem, InferenceId::QUANTIFIERS_SYGUS_STREAM_EXCLUDE_CURRENT);
  }
}

void SynthConjecture::printSynthSolutionInternal(std::ostream& out)
{
  Trace("cegqi-sol-debug") << "Printing synth solution..." << std::endl;
  Assert(d_quant[0].getNumChildren() == d_embed_quant[0].getNumChildren());
  std::vector<Node> sols;
  std::vector<int8_t> statuses;
  if (!getSynthSolutionsInternal(sols, statuses))
  {
    return;
  }
  NodeManager* nm = NodeManager::currentNM();
  for (unsigned i = 0, size = d_embed_quant[0].getNumChildren(); i < size; i++)
  {
    Node sol = sols[i];
    if (!sol.isNull())
    {
      Node prog = d_embed_quant[0][i];
      int8_t status = statuses[i];
      TypeNode tn = prog.getType();
      const DType& dt = tn.getDType();
      std::stringstream ss;
      ss << prog;
      std::string f(ss.str());
      f.erase(f.begin());
      ++(d_stats.d_solutions);

      bool is_unique_term = true;

      if (status != 0
          && (options::sygusRewSynth() || options::sygusQueryGen()
              || options::sygusFilterSolMode()
                     != options::SygusFilterSolMode::NONE))
      {
        Trace("cegqi-sol-debug") << "Run expression mining..." << std::endl;
        std::map<Node, std::unique_ptr<ExpressionMinerManager>>::iterator its =
            d_exprm.find(prog);
        if (its == d_exprm.end())
        {
          d_exprm[prog].reset(new ExpressionMinerManager(d_env));
          ExpressionMinerManager* emm = d_exprm[prog].get();
          emm->initializeSygus(
              d_tds, d_candidates[i], options::sygusSamples(), true);
          if (options::sygusRewSynth())
          {
            emm->enableRewriteRuleSynth();
          }
          if (options::sygusQueryGen())
          {
            emm->enableQueryGeneration(options::sygusQueryGenThresh());
          }
          if (options::sygusFilterSolMode()
              != options::SygusFilterSolMode::NONE)
          {
            if (options::sygusFilterSolMode()
                == options::SygusFilterSolMode::STRONG)
            {
              emm->enableFilterStrongSolutions();
            }
            else if (options::sygusFilterSolMode()
                     == options::SygusFilterSolMode::WEAK)
            {
              emm->enableFilterWeakSolutions();
            }
          }
          its = d_exprm.find(prog);
        }
        bool rew_print = false;
        is_unique_term = its->second->addTerm(sol, out, rew_print);
        if (rew_print)
        {
          ++(d_stats.d_candidate_rewrites_print);
        }
        if (!is_unique_term)
        {
          ++(d_stats.d_filtered_solutions);
        }
      }
      if (is_unique_term)
      {
        out << "(define-fun " << f << " ";
        // Only include variables that are truly bound variables of the
        // function-to-synthesize. This means we exclude variables that encode
        // external terms. This ensures that --sygus-stream prints
        // solutions with no arguments on the predicate for responses to
        // the get-abduct command.
        // pvs stores the variables that will be printed in the argument list
        // below.
        std::vector<Node> pvs;
        Node vl = dt.getSygusVarList();
        if (!vl.isNull())
        {
          Assert(vl.getKind() == BOUND_VAR_LIST);
          SygusVarToTermAttribute sta;
          for (const Node& v : vl)
          {
            if (!v.hasAttribute(sta))
            {
              pvs.push_back(v);
            }
          }
        }
        if (pvs.empty())
        {
          out << "() ";
        }
        else
        {
          vl = nm->mkNode(BOUND_VAR_LIST, pvs);
          out << vl << " ";
        }
        out << dt.getSygusType() << " ";
        if (status == 0)
        {
          out << sol;
        }
        else
        {
          Node bsol = datatypes::utils::sygusToBuiltin(sol, true);
          out << bsol;
        }
        out << ")" << std::endl;
      }
    }
  }
}

bool SynthConjecture::getSynthSolutions(
    std::map<Node, std::map<Node, Node> >& sol_map)
{
  NodeManager* nm = NodeManager::currentNM();
  std::vector<Node> sols;
  std::vector<int8_t> statuses;
  Trace("cegqi-debug") << "getSynthSolutions..." << std::endl;
  if (!getSynthSolutionsInternal(sols, statuses))
  {
    Trace("cegqi-debug") << "...failed internal" << std::endl;
    return false;
  }
  // we add it to the solution map, indexed by this conjecture
  std::map<Node, Node>& smc = sol_map[d_quant];
  for (unsigned i = 0, size = d_embed_quant[0].getNumChildren(); i < size; i++)
  {
    Node sol = sols[i];
    int8_t status = statuses[i];
    Trace("cegqi-debug") << "...got " << i << ": " << sol
                         << ", status=" << status << std::endl;
    // get the builtin solution
    Node bsol = sol;
    if (status != 0)
    {
      // Convert sygus to builtin here.
      // We must use the external representation to ensure bsol matches the
      // grammar.
      bsol = datatypes::utils::sygusToBuiltin(sol, true);
    }
    // convert to lambda
    TypeNode tn = d_embed_quant[0][i].getType();
    const DType& dt = tn.getDType();
    Node fvar = d_quant[0][i];
    Node bvl = dt.getSygusVarList();
    if (!bvl.isNull())
    {
      // since we don't have function subtyping, this assertion should only
      // check the return type
      Assert(fvar.getType().isFunction());
      Assert(fvar.getType().getRangeType().isComparableTo(bsol.getType()));
      bsol = nm->mkNode(LAMBDA, bvl, bsol);
    }
    else
    {
      Assert(fvar.getType().isComparableTo(bsol.getType()));
    }
    // store in map
    smc[fvar] = bsol;
    Trace("cegqi-debug") << "...return " << bsol << std::endl;
  }
  return true;
}

void SynthConjecture::recordSolution(std::vector<Node>& vs)
{
  Assert(vs.size() == d_candidates.size());
  d_cinfo.clear();
  for (unsigned i = 0; i < vs.size(); i++)
  {
    d_cinfo[d_candidates[i]].d_inst.push_back(vs[i]);
  }
}

bool SynthConjecture::getSynthSolutionsInternal(std::vector<Node>& sols,
                                                std::vector<int8_t>& statuses)
{
  if (!d_hasSolution)
  {
    return false;
  }
  for (unsigned i = 0, size = d_embed_quant[0].getNumChildren(); i < size; i++)
  {
    Node prog = d_embed_quant[0][i];
    Trace("cegqi-debug") << "  get solution for " << prog << std::endl;
    TypeNode tn = prog.getType();
    Assert(tn.isDatatype());
    // get the solution
    Node sol;
    int8_t status = -1;
    if (isSingleInvocation())
    {
      Assert(d_ceg_si != NULL);
      sol = d_ceg_si->getSolution(i, tn, status, true);
      if (sol.isNull())
      {
        return false;
      }
      sol = sol.getKind() == LAMBDA ? sol[1] : sol;
    }
    else
    {
      Node cprog = d_candidates[i];
      if (!d_cinfo[cprog].d_inst.empty())
      {
        // the solution is just the last instantiated term
        sol = d_cinfo[cprog].d_inst.back();
        status = 1;

        // check if there was a template
        Node sf = d_quant[0][i];
        Node templ = d_templInfer->getTemplate(sf);
        if (!templ.isNull())
        {
          Trace("cegqi-inv-debug")
              << sf << " used template : " << templ << std::endl;
          // if it was not embedded into the grammar
          if (!options::sygusTemplEmbedGrammar())
          {
            TNode templa = d_templInfer->getTemplateArg(sf);
            // make the builtin version of the full solution
            sol = d_tds->sygusToBuiltin(sol, sol.getType());
            Trace("cegqi-inv") << "Builtin version of solution is : " << sol
                               << ", type : " << sol.getType() << std::endl;
            TNode tsol = sol;
            sol = templ.substitute(templa, tsol);
            Trace("cegqi-inv-debug") << "With template : " << sol << std::endl;
            sol = Rewriter::rewrite(sol);
            Trace("cegqi-inv-debug") << "Simplified : " << sol << std::endl;
            // now, reconstruct to the syntax
            sol = d_ceg_si->reconstructToSyntax(sol, tn, status, true);
            sol = sol.getKind() == LAMBDA ? sol[1] : sol;
            Trace("cegqi-inv-debug")
                << "Reconstructed to syntax : " << sol << std::endl;
          }
          else
          {
            Trace("cegqi-inv-debug")
                << "...was embedding into grammar." << std::endl;
          }
        }
        else
        {
          Trace("cegqi-inv-debug")
              << sf << " did not use template" << std::endl;
        }
      }
      else
      {
        Trace("cegqi-warn") << "WARNING : No recorded instantiations for "
                               "syntax-guided solution!"
                            << std::endl;
      }
    }
    sols.push_back(sol);
    statuses.push_back(status);
  }
  return true;
}

Node SynthConjecture::getSymmetryBreakingPredicate(
    Node x, Node e, TypeNode tn, unsigned tindex, unsigned depth)
{
  std::vector<Node> sb_lemmas;

  // based on simple preprocessing
  Node ppred =
      d_ceg_proc->getSymmetryBreakingPredicate(x, e, tn, tindex, depth);
  if (!ppred.isNull())
  {
    sb_lemmas.push_back(ppred);
  }

  // other static conjecture-dependent symmetry breaking goes here

  if (!sb_lemmas.empty())
  {
    return sb_lemmas.size() == 1
               ? sb_lemmas[0]
               : NodeManager::currentNM()->mkNode(kind::AND, sb_lemmas);
  }
  else
  {
    return Node::null();
  }
}

ExampleEvalCache* SynthConjecture::getExampleEvalCache(Node e)
{
  EnumValueManager* eman = getEnumValueManagerFor(e);
  return eman->getExampleEvalCache();
}

}  // namespace quantifiers
}  // namespace theory
}  // namespace cvc5

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