/*********************                                                        */
/*! \file theory_arith.h
 ** \verbatim
 ** Original author: mdeters
 ** Major contributors: taking
 ** Minor contributors (to current version): ajreynol, dejan
 ** This file is part of the CVC4 prototype.
 ** Copyright (c) 2009-2012  New York University and The University of Iowa
 ** See the file COPYING in the top-level source directory for licensing
 ** information.\endverbatim
 **
 ** \brief Arithmetic theory.
 ** ** Arithmetic theory.
 **/

#include "cvc4_private.h"

#ifndef __CVC4__THEORY__ARITH__THEORY_ARITH_H
#define __CVC4__THEORY__ARITH__THEORY_ARITH_H

#include "theory/theory.h"
#include "context/context.h"
#include "context/cdlist.h"
#include "context/cdhashset.h"
#include "context/cdinsert_hashmap.h"
#include "context/cdqueue.h"
#include "expr/node.h"

#include "util/dense_map.h"

#include "theory/arith/arithvar.h"
#include "theory/arith/delta_rational.h"
#include "theory/arith/matrix.h"
#include "theory/arith/arith_rewriter.h"
#include "theory/arith/partial_model.h"
#include "theory/arith/linear_equality.h"
#include "theory/arith/simplex.h"
#include "theory/arith/arith_static_learner.h"
#include "theory/arith/arithvar_node_map.h"
#include "theory/arith/dio_solver.h"
#include "theory/arith/congruence_manager.h"

#include "theory/arith/constraint.h"

#include "util/statistics_registry.h"
#include "util/result.h"

#include <vector>
#include <map>
#include <queue>

namespace CVC4 {
namespace theory {

namespace quantifiers {
  class InstStrategySimplex;
}

namespace arith {

/**
 * Implementation of QF_LRA.
 * Based upon:
 * http://research.microsoft.com/en-us/um/people/leonardo/cav06.pdf
 */
class TheoryArith : public Theory {
  friend class quantifiers::InstStrategySimplex;
private:
  bool d_nlIncomplete;
  // TODO A better would be:
  //context::CDO<bool> d_nlIncomplete;

  enum Result::Sat d_qflraStatus;
  // check()
  //   !done() -> d_qflraStatus = Unknown
  //   fullEffort(e) -> simplex returns either sat or unsat
  //   !fullEffort(e) -> simplex returns either sat, unsat or unknown
  //                     if unknown, save the assignment
  //                     if unknown, the simplex priority queue cannot be emptied
  int d_unknownsInARow;


  /**
   * This counter is false if nothing has been done since the last cut.
   * This is used to break an infinite loop.
   */
  bool d_hasDoneWorkSinceCut;

  /** Static learner. */
  ArithStaticLearner d_learner;


  ArithVar d_numberOfVariables;
  inline ArithVar getNumberOfVariables() const { return d_numberOfVariables; }
  std::vector<ArithVar> d_pool;
  void releaseArithVar(ArithVar v);

  /**
   * The map between arith variables to nodes.
   */
  ArithVarNodeMap d_arithvarNodeMap;

  typedef ArithVarNodeMap::var_iterator var_iterator;
  var_iterator var_begin() const { return d_arithvarNodeMap.var_begin(); }
  var_iterator var_end() const { return d_arithvarNodeMap.var_end(); }

  NodeSet d_setupNodes;
  bool isSetup(Node n) const {
    return d_setupNodes.find(n) != d_setupNodes.end();
  }
  void markSetup(Node n){
    Assert(!isSetup(n));
    d_setupNodes.insert(n);
  }

  void setupDivLike(const Variable& x);

  void setupVariable(const Variable& x);
  void setupVariableList(const VarList& vl);
  void setupPolynomial(const Polynomial& poly);
  void setupAtom(TNode atom);

  void cautiousSetupPolynomial(const Polynomial& p);

  class SetupLiteralCallBack : public TNodeCallBack {
  private:
    TheoryArith* d_arith;
  public:
    SetupLiteralCallBack(TheoryArith* ta) : d_arith(ta){}
    void operator()(TNode lit){
      TNode atom = (lit.getKind() == kind::NOT) ? lit[0] : lit;
      if(!d_arith->isSetup(atom)){
        d_arith->setupAtom(atom);
      }
    }
  } d_setupLiteralCallback;

  /**
   * A superset of all of the assertions that currently are not the literal for
   * their constraint do not match constraint literals. Not just the witnesses.
   */
  context::CDInsertHashMap<Node, Constraint, NodeHashFunction> d_assertionsThatDoNotMatchTheirLiterals;

  /**
   * (For the moment) the type hierarchy goes as:
   * Integer <: Real
   * The type number of a variable is an integer representing the most specific
   * type of the variable. The possible values of type number are:
   */
  enum ArithType
    {
      ATReal = 0,
      ATInteger = 1
   };

  std::vector<ArithType> d_variableTypes;
  inline ArithType nodeToArithType(TNode x) const {
    return (x.getType().isInteger() ? ATInteger : ATReal);
  }

  /** Returns true if x is of type Integer. */
  inline bool isInteger(ArithVar x) const {
    return d_variableTypes[x] >= ATInteger;
  }

  /** This is the set of variables initially introduced as slack variables. */
  std::vector<bool> d_slackVars;

  /** Returns true if the variable was initially introduced as a slack variable. */
  inline bool isSlackVariable(ArithVar x) const{
    return d_slackVars[x];
  }

  /**
   * On full effort checks (after determining LA(Q) satisfiability), we
   * consider integer vars, but we make sure to do so fairly to avoid
   * nontermination (although this isn't a guarantee).  To do it fairly,
   * we consider variables in round-robin fashion.  This is the
   * round-robin index.
   */
  ArithVar d_nextIntegerCheckVar;

  /**
   * Queue of Integer variables that are known to be equal to a constant.
   */
  context::CDQueue<ArithVar> d_constantIntegerVariables;

  Node callDioSolver();
  Node dioCutting();

  Comparison mkIntegerEqualityFromAssignment(ArithVar v);

  /**
   * List of all of the disequalities asserted in the current context that are not known
   * to be satisfied.
   */
  context::CDQueue<Constraint> d_diseqQueue;

  /**
   * Constraints that have yet to be processed by proagation work list.
   * All of the elements have type of LowerBound, UpperBound, or
   * Equality.
   *
   * This is empty at the beginning of every check call.
   *
   * If head()->getType() == LowerBound or UpperBound,
   * then d_cPL[1] is the previous constraint in d_partialModel for the
   * corresponding bound.
   * If head()->getType() == Equality,
   * then d_cPL[1] is the previous lowerBound in d_partialModel,
   * and d_cPL[2] is the previous upperBound in d_partialModel.
   */
  std::deque<Constraint> d_currentPropagationList;

  context::CDQueue<Constraint> d_learnedBounds;

  /**
   * Manages information about the assignment and upper and lower bounds on
   * variables.
   */
  ArithPartialModel d_partialModel;

  /**
   * The tableau for all of the constraints seen thus far in the system.
   */
  Tableau d_tableau;

  /**
   * Maintains the relationship between the PartialModel and the Tableau.
   */
  LinearEqualityModule d_linEq;

  /**
   * A Diophantine equation solver.  Accesses the tableau and partial
   * model (each in a read-only fashion).
   */
  DioSolver d_diosolver;

  /** Counts the number of notifyRestart() calls to the theory. */
  uint32_t d_restartsCounter;

  /**
   * Every number of restarts equal to s_TABLEAU_RESET_PERIOD,
   * the density of the tableau, d, is computed.
   * If d >= s_TABLEAU_RESET_DENSITY * d_initialDensity, the tableau
   * is set to d_initialTableau.
   */
  bool d_tableauSizeHasBeenModified;
  double d_tableauResetDensity;
  uint32_t d_tableauResetPeriod;
  static const uint32_t s_TABLEAU_RESET_INCREMENT = 5;


  /** This is only used by simplex at the moment. */
  context::CDList<Node> d_conflicts;
  class PushCallBack : public NodeCallBack {
  private:
    context::CDList<Node>& d_list;
  public:
    PushCallBack(context::CDList<Node>& l)
    : d_list(l)
    {}
    void operator()(Node n){
      d_list.push_back(n);
    }
  } d_raiseConflict;

  /** Returns true iff a conflict has been raised. */
  inline bool inConflict() const {
    return !d_conflicts.empty();
  }
  /**
   * Outputs the contents of d_conflicts onto d_out.
   * Must be inConflict().
   */
  void outputConflicts();


  class TempVarMalloc : public ArithVarMalloc {
  private:
    TheoryArith& d_ta;
  public:
    TempVarMalloc(TheoryArith& ta) : d_ta(ta) {}
    ArithVar request(){
      Node skolem = mkRealSkolem("tmpVar");
      return d_ta.requestArithVar(skolem, false);
    }
    void release(ArithVar v){ d_ta.releaseArithVar(v); }
  } d_tempVarMalloc;

  /**
   * A copy of the tableau.
   * This is equivalent  to the original tableau if d_tableauSizeHasBeenModified
   * is false.
   * The set of basic and non-basic variables may differ from d_tableau.
   */
  Tableau d_smallTableauCopy;

  /**
   * Returns true if all of the basic variables in the simplex queue of
   * basic variables that violate their bounds in the current tableau
   * are basic in d_smallTableauCopy.
   *
   * d_tableauSizeHasBeenModified must be false when calling this.
   * Simplex's priority queue must be in collection mode.
   */
  bool safeToReset() const;

  /** This keeps track of difference equalities. Mostly for sharing. */
  ArithCongruenceManager d_congruenceManager;

  /** This implements the Simplex decision procedure. */
  SimplexDecisionProcedure d_simplex;


  /** The constraint database associated with the theory. */
  ConstraintDatabase d_constraintDatabase;

  class ModelException : public Exception {
  public:
    ModelException(TNode n, const char* msg) throw ();
    virtual ~ModelException() throw ();
  };

  /** Internal model value for the node */
  DeltaRational getDeltaValue(TNode n) const throw (DeltaRationalException, ModelException);

  /** Uninterpretted function symbol for use when interpreting
   * division by zero.
   */
  Node d_realDivideBy0Func;
  Node d_intDivideBy0Func;
  Node d_intModulusBy0Func;
  Node getRealDivideBy0Func();
  Node getIntDivideBy0Func();
  Node getIntModulusBy0Func();

  Node definingIteForDivLike(Node divLike);
  Node axiomIteForTotalDivision(Node div_tot);
  Node axiomIteForTotalIntDivision(Node int_div_like);


  class DeltaComputeCallback : public RationalCallBack {
  private:
    const TheoryArith* d_ta;
  public:
    DeltaComputeCallback(const TheoryArith* ta) : d_ta(ta){}

    Rational operator()() const{
      return d_ta->deltaValueForTotalOrder();
    }
  } d_deltaComputeCallback;

public:
  TheoryArith(context::Context* c, context::UserContext* u, OutputChannel& out, Valuation valuation, const LogicInfo& logicInfo, QuantifiersEngine* qe);
  virtual ~TheoryArith();

  /**
   * Does non-context dependent setup for a node connected to a theory.
   */
  void preRegisterTerm(TNode n);

  void setMasterEqualityEngine(eq::EqualityEngine* eq);

  void check(Effort e);
  void propagate(Effort e);
  Node explain(TNode n);

  Rational deltaValueForTotalOrder() const;
  void collectModelInfo( TheoryModel* m, bool fullModel );

  void shutdown(){ }

  void presolve();
  void notifyRestart();
  PPAssertStatus ppAssert(TNode in, SubstitutionMap& outSubstitutions);
  Node ppRewrite(TNode atom);
  void ppStaticLearn(TNode in, NodeBuilder<>& learned);

  std::string identify() const { return std::string("TheoryArith"); }

  EqualityStatus getEqualityStatus(TNode a, TNode b);

  void addSharedTerm(TNode n);

private:

  class BasicVarModelUpdateCallBack : public ArithVarCallBack{
  private:
    SimplexDecisionProcedure& d_simplex;

  public:
    BasicVarModelUpdateCallBack(SimplexDecisionProcedure& s):
      d_simplex(s)
    {}

    void operator()(ArithVar x){
      d_simplex.updateBasic(x);
    }
  };

  BasicVarModelUpdateCallBack d_basicVarModelUpdateCallBack;

  /** The constant zero. */
  DeltaRational d_DELTA_ZERO;

  /** propagates an arithvar */
  void propagateArithVar(bool upperbound, ArithVar var );

  /**
   * Using the simpleKind return the ArithVar associated with the assertion.
   */
  ArithVar determineArithVar(const Polynomial& p) const;
  ArithVar determineArithVar(TNode assertion) const;

  /**
   * Splits the disequalities in d_diseq that are violated using lemmas on demand.
   * returns true if any lemmas were issued.
   * returns false if all disequalities are satisfied in the current model.
   */
  bool splitDisequalities();

  /** A Difference variable is known to be 0.*/
  void zeroDifferenceDetected(ArithVar x);


  /**
   * Looks for the next integer variable without an integer assignment in a round robin fashion.
   * Changes the value of d_nextIntegerCheckVar.
   *
   * If this returns false, d_nextIntegerCheckVar does not have an integer assignment.
   * If this returns true, all integer variables have an integer assignment.
   */
  bool hasIntegerModel();

  /**
   * Issues branches for non-slack integer variables with non-integer assignments.
   * Returns a cut for a lemma.
   * If there is an integer model, this returns Node::null().
   */
  Node roundRobinBranch();

  /**
   * This requests a new unique ArithVar value for x.
   * This also does initial (not context dependent) set up for a variable,
   * except for setting up the initial.
   */
  ArithVar requestArithVar(TNode x, bool slack);

  /** Initial (not context dependent) sets up for a variable.*/
  void setupBasicValue(ArithVar x);

  /** Initial (not context dependent) sets up for a new slack variable.*/
  void setupSlack(TNode left);


  /**
   * Assert*(n, orig) takes an bound n that is implied by orig.
   * and asserts that as a new bound if it is tighter than the current bound
   * and updates the value of a basic variable if needed.
   *
   * orig must be a literal in the SAT solver so that it can be used for
   * conflict analysis.
   *
   * x is the variable getting the new bound,
   * c is the value of the new bound.
   *
   * If this new bound is in conflict with the other bound,
   * a node describing this conflict is returned.
   * If this new bound is not in conflict, Node::null() is returned.
   */
  bool AssertLower(Constraint constraint);
  bool AssertUpper(Constraint constraint);
  bool AssertEquality(Constraint constraint);
  bool AssertDisequality(Constraint constraint);

  /** Tracks the bounds that were updated in the current round. */
  DenseSet d_updatedBounds;

  /** Tracks the basic variables where propagation might be possible. */
  DenseSet d_candidateBasics;

  bool hasAnyUpdates() { return !d_updatedBounds.empty(); }
  void clearUpdates();

  void revertOutOfConflict();

  void propagateCandidates();
  void propagateCandidate(ArithVar basic);
  bool propagateCandidateBound(ArithVar basic, bool upperBound);

  inline bool propagateCandidateLowerBound(ArithVar basic){
    return propagateCandidateBound(basic, false);
  }
  inline bool propagateCandidateUpperBound(ArithVar basic){
    return propagateCandidateBound(basic, true);
  }

  /**
   * Performs a check to see if it is definitely true that setup can be avoided.
   */
  bool canSafelyAvoidEqualitySetup(TNode equality);

  /**
   * Handles the case splitting for check() for a new assertion.
   * Returns a conflict if one was found.
   * Returns Node::null if no conflict was found.
   */
  Constraint constraintFromFactQueue();
  bool assertionCases(Constraint c);

  /**
   * Returns the basic variable with the shorted row containing a non-basic variable.
   * If no such row exists, return ARITHVAR_SENTINEL.
   */
  ArithVar findShortestBasicRow(ArithVar variable);

  /**
   * Debugging only routine!
   * Returns true iff every variable is consistent in the partial model.
   */
  bool entireStateIsConsistent(const std::string& locationHint);
  bool unenqueuedVariablesAreConsistent();

  bool isImpliedUpperBound(ArithVar var, Node exp);
  bool isImpliedLowerBound(ArithVar var, Node exp);

  void internalExplain(TNode n, NodeBuilder<>& explainBuilder);


  void asVectors(const Polynomial& p,
                 std::vector<Rational>& coeffs,
                 std::vector<ArithVar>& variables);

  /** Routine for debugging. Print the assertions the theory is aware of. */
  void debugPrintAssertions();
  /** Debugging only routine. Prints the model. */
  void debugPrintModel();

  /** Counts the number of fullCheck calls to arithmetic. */
  uint32_t d_fullCheckCounter;
  std::vector<Node> cutAllBounded() const;
  Node branchIntegerVariable(ArithVar x) const;

  /** These fields are designed to be accessible to TheoryArith methods. */
  class Statistics {
  public:
    IntStat d_statAssertUpperConflicts, d_statAssertLowerConflicts;

    IntStat d_statUserVariables, d_statSlackVariables;
    IntStat d_statDisequalitySplits;
    IntStat d_statDisequalityConflicts;
    TimerStat d_simplifyTimer;
    TimerStat d_staticLearningTimer;

    TimerStat d_presolveTime;

    TimerStat d_newPropTime;

    IntStat d_externalBranchAndBounds;

    IntStat d_initialTableauSize;
    IntStat d_currSetToSmaller;
    IntStat d_smallerSetToCurr;
    TimerStat d_restartTimer;

    TimerStat d_boundComputationTime;
    IntStat d_boundComputations, d_boundPropagations;

    IntStat d_unknownChecks;
    IntStat d_maxUnknownsInARow;
    AverageStat d_avgUnknownsInARow;

    IntStat d_revertsOnConflicts;
    IntStat d_commitsOnConflicts;
    IntStat d_nontrivialSatChecks;

    Statistics();
    ~Statistics();
  };

  Statistics d_statistics;


};/* class TheoryArith */

}/* CVC4::theory::arith namespace */
}/* CVC4::theory namespace */
}/* CVC4 namespace */

#endif /* __CVC4__THEORY__ARITH__THEORY_ARITH_H */