/*********************                                                        */
/*! \file ho_trigger.cpp
 ** \verbatim
 ** Top contributors (to current version):
 **   Andrew Reynolds
 ** This file is part of the CVC4 project.
 ** Copyright (c) 2009-2019 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 higher-order trigger class
 **/

#include <stack>

#include "theory/quantifiers/ematching/ho_trigger.h"
#include "theory/quantifiers/instantiate.h"
#include "theory/quantifiers/term_database.h"
#include "theory/quantifiers/term_util.h"
#include "theory/quantifiers_engine.h"
#include "theory/theory_engine.h"
#include "theory/uf/equality_engine.h"
#include "theory/uf/theory_uf_rewriter.h"
#include "util/hash.h"

using namespace CVC4::kind;

namespace CVC4 {
namespace theory {
namespace inst {

HigherOrderTrigger::HigherOrderTrigger(
    QuantifiersEngine* qe,
    Node q,
    std::vector<Node>& nodes,
    std::map<Node, std::vector<Node> >& ho_apps)
    : Trigger(qe, q, nodes), d_ho_var_apps(ho_apps)
{
  NodeManager* nm = NodeManager::currentNM();
  // process the higher-order variable applications
  for (std::pair<const Node, std::vector<Node> >& as : d_ho_var_apps)
  {
    Node n = as.first;
    d_ho_var_list.push_back(n);
    TypeNode tn = n.getType();
    Assert(tn.isFunction());
    if (Trace.isOn("ho-quant-trigger"))
    {
      Trace("ho-quant-trigger") << "  have " << as.second.size();
      Trace("ho-quant-trigger") << " patterns with variable operator " << n
                                << ":" << std::endl;
      for (unsigned j = 0; j < as.second.size(); j++)
      {
        Trace("ho-quant-trigger") << "  " << as.second[j] << std::endl;
      }
    }
    if (d_ho_var_types.find(tn) == d_ho_var_types.end())
    {
      Trace("ho-quant-trigger") << "  type " << tn
                                << " needs higher-order matching." << std::endl;
      d_ho_var_types.insert(tn);
    }
    // make the bound variable lists
    d_ho_var_bvl[n] = nm->getBoundVarListForFunctionType(tn);
    for (const Node& nc : d_ho_var_bvl[n])
    {
      d_ho_var_bvs[n].push_back(nc);
    }
  }
}

HigherOrderTrigger::~HigherOrderTrigger() {}
void HigherOrderTrigger::collectHoVarApplyTerms(
    Node q, Node& n, std::map<Node, std::vector<Node> >& apps)
{
  std::vector<Node> ns;
  ns.push_back(n);
  collectHoVarApplyTerms(q, ns, apps);
  Assert(ns.size() == 1);
  n = ns[0];
}

void HigherOrderTrigger::collectHoVarApplyTerms(
    Node q, std::vector<Node>& ns, std::map<Node, std::vector<Node> >& apps)
{
  std::unordered_map<TNode, Node, TNodeHashFunction> visited;
  std::unordered_map<TNode, Node, TNodeHashFunction>::iterator it;
  // whether the visited node is a child of a HO_APPLY chain
  std::unordered_map<TNode, bool, TNodeHashFunction> withinApply;
  std::vector<TNode> visit;
  TNode cur;
  for (unsigned i = 0, size = ns.size(); i < size; i++)
  {
    visit.push_back(ns[i]);
    withinApply[ns[i]] = false;
    do
    {
      cur = visit.back();
      visit.pop_back();

      it = visited.find(cur);
      if (it == visited.end())
      {
        // do not look in nested quantifiers
        if (cur.getKind() == FORALL)
        {
          visited[cur] = cur;
        }
        else
        {
          bool curWithinApply = withinApply[cur];
          visited[cur] = Node::null();
          visit.push_back(cur);
          for (unsigned j = 0, sizec = cur.getNumChildren(); j < sizec; j++)
          {
            withinApply[cur[j]] = curWithinApply && j == 0;
            visit.push_back(cur[j]);
          }
        }
      }
      else if (it->second.isNull())
      {
        // carry the conversion
        Node ret = cur;
        bool childChanged = false;
        std::vector<Node> children;
        if (cur.getMetaKind() == kind::metakind::PARAMETERIZED)
        {
          children.push_back(cur.getOperator());
        }
        for (const Node& nc : cur)
        {
          it = visited.find(nc);
          Assert(it != visited.end());
          Assert(!it->second.isNull());
          childChanged = childChanged || nc != it->second;
          children.push_back(it->second);
        }
        if (childChanged)
        {
          ret = NodeManager::currentNM()->mkNode(cur.getKind(), children);
        }
        // now, convert and store the application
        if (!withinApply[cur])
        {
          TNode op;
          if (ret.getKind() == kind::APPLY_UF)
          {
            // could be a fully applied function variable
            op = ret.getOperator();
          }
          else if (ret.getKind() == kind::HO_APPLY)
          {
            op = ret;
            while (op.getKind() == kind::HO_APPLY)
            {
              op = op[0];
            }
          }
          if (!op.isNull())
          {
            if (op.getKind() == kind::INST_CONSTANT)
            {
              Assert(quantifiers::TermUtil::getInstConstAttr(ret) == q);
              Trace("ho-quant-trigger-debug")
                  << "Ho variable apply term : " << ret << " with head " << op
                  << std::endl;
              if (ret.getKind() == kind::APPLY_UF)
              {
                Node prev = ret;
                // for consistency, convert to HO_APPLY if fully applied
                ret = uf::TheoryUfRewriter::getHoApplyForApplyUf(ret);
              }
              apps[op].push_back(ret);
            }
          }
        }
        visited[cur] = ret;
      }
    } while (!visit.empty());

    // store the conversion
    Assert(visited.find(ns[i]) != visited.end());
    ns[i] = visited[ns[i]];
  }
}

int HigherOrderTrigger::addInstantiations()
{
  // call the base class implementation
  int addedFoLemmas = Trigger::addInstantiations();
  // also adds predicate lemms to force app completion
  int addedHoLemmas = addHoTypeMatchPredicateLemmas();
  return addedHoLemmas + addedFoLemmas;
}

bool HigherOrderTrigger::sendInstantiation(InstMatch& m)
{
  if (options::hoMatching())
  {
    // get substitution corresponding to m
    std::vector<TNode> vars;
    std::vector<TNode> subs;
    quantifiers::TermUtil* tutil = d_quantEngine->getTermUtil();
    for (unsigned i = 0, size = d_quant[0].getNumChildren(); i < size; i++)
    {
      subs.push_back(m.d_vals[i]);
      vars.push_back(tutil->getInstantiationConstant(d_quant, i));
    }

    Trace("ho-unif-debug") << "Run higher-order unification..." << std::endl;

    // get the substituted form of all variable-operator ho application terms
    std::map<TNode, std::vector<Node> > ho_var_apps_subs;
    for (std::pair<const Node, std::vector<Node> >& ha : d_ho_var_apps)
    {
      TNode var = ha.first;
      for (unsigned j = 0, size = ha.second.size(); j < size; j++)
      {
        TNode app = ha.second[j];
        Node sapp =
            app.substitute(vars.begin(), vars.end(), subs.begin(), subs.end());
        ho_var_apps_subs[var].push_back(sapp);
        Trace("ho-unif-debug") << "  app[" << var << "] : " << app << " -> "
                               << sapp << std::endl;
      }
    }

    // compute argument vectors for each variable
    d_lchildren.clear();
    d_arg_to_arg_rep.clear();
    d_arg_vector.clear();
    EqualityQuery* eq = d_quantEngine->getEqualityQuery();
    for (std::pair<const TNode, std::vector<Node> >& ha : ho_var_apps_subs)
    {
      TNode var = ha.first;
      unsigned vnum = var.getAttribute(InstVarNumAttribute());
      TNode value = m.d_vals[vnum];
      Trace("ho-unif-debug") << "  val[" << var << "] = " << value << std::endl;

      Trace("ho-unif-debug2") << "initialize lambda information..."
                              << std::endl;
      // initialize the lambda children
      d_lchildren[vnum].push_back(value);
      std::map<TNode, std::vector<Node> >::iterator ithb =
          d_ho_var_bvs.find(var);
      Assert(ithb != d_ho_var_bvs.end());
      d_lchildren[vnum].insert(
          d_lchildren[vnum].end(), ithb->second.begin(), ithb->second.end());

      Trace("ho-unif-debug2") << "compute fixed arguments..." << std::endl;
      // compute for each argument if it is only applied to a fixed value modulo
      // equality
      std::map<unsigned, Node> fixed_vals;
      for (unsigned i = 0; i < ha.second.size(); i++)
      {
        std::vector<TNode> args;
        // must substitute the operator we matched with the original
        // higher-order variable (var) that matched it. This ensures that the
        // argument vector (args) below is of the proper length. This handles,
        // for example, matches like:
        //   (@ x y) with (@ (@ k1 k2) k3)
        // where k3 but not k2 should be an argument of the match.
        Node hmatch = ha.second[i];
        Trace("ho-unif-debug2") << "Match is " << hmatch << std::endl;
        hmatch = hmatch.substitute(value, var);
        Trace("ho-unif-debug2") << "Pre-subs match is " << hmatch << std::endl;
        Node f = uf::TheoryUfRewriter::decomposeHoApply(hmatch, args);
        // Assert( f==value );
        for (unsigned k = 0, size = args.size(); k < size; k++)
        {
          // must now subsitute back, to handle cases like
          // (@ x y) matching (@ t (@ t s))
          // where the above substitution would produce (@ x (@ x s)),
          // but the argument should be (@ t s).
          args[k] = args[k].substitute(var, value);
          Node val = args[k];
          std::map<unsigned, Node>::iterator itf = fixed_vals.find(k);
          if (itf == fixed_vals.end())
          {
            fixed_vals[k] = val;
          }
          else if (!itf->second.isNull())
          {
            if (!eq->areEqual(itf->second, args[k]))
            {
              if (!d_quantEngine->getTermDatabase()->isEntailed(
                      itf->second.eqNode(args[k]), true, eq))
              {
                fixed_vals[k] = Node::null();
              }
            }
          }
        }
      }
      if (Trace.isOn("ho-unif-debug"))
      {
        for (std::map<unsigned, Node>::iterator itf = fixed_vals.begin();
             itf != fixed_vals.end();
             ++itf)
        {
          Trace("ho-unif-debug") << "  arg[" << var << "][" << itf->first
                                 << "] : " << itf->second << std::endl;
        }
      }

      // now construct argument vectors
      Trace("ho-unif-debug2") << "compute argument vectors..." << std::endl;
      std::map<Node, unsigned> arg_to_rep;
      for (unsigned index = 0, size = ithb->second.size(); index < size;
           index++)
      {
        Node bv_at_index = ithb->second[index];
        std::map<unsigned, Node>::iterator itf = fixed_vals.find(index);
        Trace("ho-unif-debug") << "  * arg[" << var << "][" << index << "]";
        if (itf != fixed_vals.end())
        {
          if (!itf->second.isNull())
          {
            Node r = eq->getRepresentative(itf->second);
            std::map<Node, unsigned>::iterator itfr = arg_to_rep.find(r);
            if (itfr != arg_to_rep.end())
            {
              d_arg_to_arg_rep[vnum][index] = itfr->second;
              // function applied to equivalent values at multiple arguments,
              // can permute variables
              d_arg_vector[vnum][itfr->second].push_back(bv_at_index);
              Trace("ho-unif-debug") << " = { self } ++ arg[" << var << "]["
                                     << itfr->second << "]" << std::endl;
            }
            else
            {
              arg_to_rep[r] = index;
              // function applied to single value, can either use variable or
              // value at this argument position
              d_arg_vector[vnum][index].push_back(bv_at_index);
              d_arg_vector[vnum][index].push_back(itf->second);
              if (!options::hoMatchingVarArgPriority())
              {
                std::reverse(d_arg_vector[vnum][index].begin(),
                             d_arg_vector[vnum][index].end());
              }
              Trace("ho-unif-debug") << " = { self, " << itf->second << " } "
                                     << std::endl;
            }
          }
          else
          {
            // function is applied to disequal values, can only use variable at
            // this argument position
            d_arg_vector[vnum][index].push_back(bv_at_index);
            Trace("ho-unif-debug") << " = { self } (disequal)" << std::endl;
          }
        }
        else
        {
          // argument is irrelevant to matching, assume identity variable
          d_arg_vector[vnum][index].push_back(bv_at_index);
          Trace("ho-unif-debug") << " = { self } (irrelevant)" << std::endl;
        }
      }
      Trace("ho-unif-debug2") << "finished." << std::endl;
    }

    bool ret = sendInstantiation(m, 0);
    Trace("ho-unif-debug") << "Finished, success = " << ret << std::endl;
    return ret;
  }
  else
  {
    // do not run higher-order matching
    return d_quantEngine->getInstantiate()->addInstantiation(d_quant, m);
  }
}

// recursion depth limited by number of arguments of higher order variables
// occurring as pattern operators (very small)
bool HigherOrderTrigger::sendInstantiation(InstMatch& m, unsigned var_index)
{
  Trace("ho-unif-debug2") << "send inst " << var_index << " / "
                          << d_ho_var_list.size() << std::endl;
  if (var_index == d_ho_var_list.size())
  {
    // we now have an instantiation to try
    return d_quantEngine->getInstantiate()->addInstantiation(d_quant, m);
  }
  else
  {
    Node var = d_ho_var_list[var_index];
    unsigned vnum = var.getAttribute(InstVarNumAttribute());
    Assert(vnum < m.d_vals.size());
    Node value = m.d_vals[vnum];
    Assert(d_lchildren[vnum][0] == value);
    Assert(d_ho_var_bvl.find(var) != d_ho_var_bvl.end());

    // now, recurse on arguments to enumerate equivalent matching lambda
    // expressions
    bool ret =
        sendInstantiationArg(m, var_index, vnum, 0, d_ho_var_bvl[var], false);

    // reset the value
    m.d_vals[vnum] = value;

    return ret;
  }
}

bool HigherOrderTrigger::sendInstantiationArg(InstMatch& m,
                                              unsigned var_index,
                                              unsigned vnum,
                                              unsigned arg_index,
                                              Node lbvl,
                                              bool arg_changed)
{
  Trace("ho-unif-debug2") << "send inst arg " << arg_index << " / "
                          << lbvl.getNumChildren() << std::endl;
  if (arg_index == lbvl.getNumChildren())
  {
    // construct the lambda
    if (arg_changed)
    {
      Trace("ho-unif-debug2")
          << "  make lambda from children: " << d_lchildren[vnum] << std::endl;
      Node body =
          NodeManager::currentNM()->mkNode(kind::APPLY_UF, d_lchildren[vnum]);
      Trace("ho-unif-debug2") << "  got " << body << std::endl;
      Node lam = NodeManager::currentNM()->mkNode(kind::LAMBDA, lbvl, body);
      m.d_vals[vnum] = lam;
      Trace("ho-unif-debug2") << "  try " << vnum << " -> " << lam << std::endl;
    }
    return sendInstantiation(m, var_index + 1);
  }
  else
  {
    std::map<unsigned, unsigned>::iterator itr =
        d_arg_to_arg_rep[vnum].find(arg_index);
    unsigned rindex =
        itr != d_arg_to_arg_rep[vnum].end() ? itr->second : arg_index;
    std::map<unsigned, std::vector<Node> >::iterator itv =
        d_arg_vector[vnum].find(rindex);
    Assert(itv != d_arg_vector[vnum].end());
    Node prev = lbvl[arg_index];
    bool ret = false;
    // try each argument in the vector
    for (unsigned i = 0, size = itv->second.size(); i < size; i++)
    {
      bool new_arg_changed = arg_changed || prev != itv->second[i];
      d_lchildren[vnum][arg_index + 1] = itv->second[i];
      if (sendInstantiationArg(
              m, var_index, vnum, arg_index + 1, lbvl, new_arg_changed))
      {
        ret = true;
        break;
      }
    }
    // clean up
    d_lchildren[vnum][arg_index + 1] = prev;
    return ret;
  }
}

int HigherOrderTrigger::addHoTypeMatchPredicateLemmas()
{
  if (d_ho_var_types.empty())
  {
    return 0;
  }
  Trace("ho-quant-trigger") << "addHoTypeMatchPredicateLemmas..." << std::endl;
  unsigned numLemmas = 0;
  // this forces expansion of APPLY_UF terms to curried HO_APPLY chains
  quantifiers::TermDb* tdb = d_quantEngine->getTermDatabase();
  unsigned size = tdb->getNumOperators();
  NodeManager* nm = NodeManager::currentNM();
  for (unsigned j = 0; j < size; j++)
  {
    Node f = tdb->getOperator(j);
    if (f.isVar())
    {
      TypeNode tn = f.getType();
      if (tn.isFunction())
      {
        std::vector<TypeNode> argTypes = tn.getArgTypes();
        Assert(argTypes.size() > 0);
        TypeNode range = tn.getRangeType();
        // for each function type suffix of the type of f, for example if
        // f : (Int -> (Int -> Int))
        // we iterate with stn = (Int -> (Int -> Int)) and (Int -> Int)
        for (unsigned a = 0, arg_size = argTypes.size(); a < arg_size; a++)
        {
          std::vector<TypeNode> sargts;
          sargts.insert(sargts.begin(), argTypes.begin() + a, argTypes.end());
          Assert(sargts.size() > 0);
          TypeNode stn = nm->mkFunctionType(sargts, range);
          Trace("ho-quant-trigger-debug")
              << "For " << f << ", check " << stn << "..." << std::endl;
          // if a variable of this type occurs in this trigger
          if (d_ho_var_types.find(stn) != d_ho_var_types.end())
          {
            Node u = tdb->getHoTypeMatchPredicate(tn);
            Node au = nm->mkNode(kind::APPLY_UF, u, f);
            if (d_quantEngine->addLemma(au))
            {
              // this forces f to be a first-class member of the quantifier-free
              // equality engine, which in turn forces the quantifier-free
              // theory solver to expand it to an HO_APPLY chain.
              Trace("ho-quant")
                  << "Added ho match predicate lemma : " << au << std::endl;
              numLemmas++;
            }
          }
        }
      }
    }
  }

  return numLemmas;
}

} /* CVC4::theory::inst namespace */
} /* CVC4::theory namespace */
} /* CVC4 namespace */