formula_checker.h

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// Author(s): Luc Engelen
// Copyright: see the accompanying file COPYING or copy at
// https://github.com/mCRL2org/mCRL2/blob/master/COPYING
//
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//
/// \file mcrl2/data/detail/prover/formula_checker.h
/// \brief Interface to class Formula_Checker
 
#ifndef FORMULA_CHECKER_H
#define FORMULA_CHECKER_H
 
#include "mcrl2/data/detail/prover/bdd_prover.h"
#include "mcrl2/data/detail/prover/bdd2dot.h"
 
namespace mcrl2::data::detail
{
 
/// \brief The class formula checker takes a data specification in mCRL2 format and a list of expressions
/// \brief of sort Bool in the mCRL2 format and determines whether or not these expersions are tautologies or
/// \brief contradictions.
/// The class Formula_Checker is initialized with a specification of data equations in internal mCRL2 format using the
/// \brief Constructor Formula_Checker::Formula_Checker. After initialization, the function Formula_Checker::check_formulas can
/// be called any number of times to check whether the expressions of sort Bool in internal mCRL2 format in the list
/// passed as parameter a_formulas are tautologies or contradictions.
///
/// The class Formula_Checker uses an instance of the class BDD_Prover to prove a number of propositional formulas. The
/// prover is initialized with the parameters a_rewrite_strategy, a_time_limit, a_path_eliminator, a_solver_type,
/// a_apply_induction and a_lps. The parameter a_rewrite_strategy specifies which rewrite strategy is used by the prover's
/// rewriter. It can be set to either GS_REWR_JITTY or GS_REWR_JITTYC. The parameter
/// a_time_limit specifies the maximum amount of time in seconds to be spent by the prover on proving a single formula. If
/// a_time_limit is set to 0, no time limit will be enforced. The parameter a_path_eliminator specifies whether or not
/// path elimination is applied. When path elimination is applied, the prover uses an SMT solver to remove inconsistent
/// paths from BDDs. The parameter a_solver_type specifies which SMT solver is used for path elimination. Either the SMT
/// solver ario (http://www.eecs.umich.edu/~ario/) or cvc-lite (http://www.cs.nyu.edu/acsys/cvcl/) can be used. To use one
/// of these solvers, the directory containing the corresponding executable must be in the path. If the parameter
/// a_path_eliminator is set to false, the parameter a_solver_type is ignored. The parameter a_time_limit specifies the
/// data equations used by the prover's rewriter. The parameter a_apply_induction indicates whether or not induction on
/// list will be applied.
///
/// The parameter a_dot_file_name specifies whether a file in dot format of the resulting BDD is saved each time the
/// prover cannot determine whether an expression of sort Bool is a contradiction or a tautology. If the parameter is set
/// to 0, no .dot files are saved. If a string is passed as parameter a_dot_file_name, this string will be used as the
/// prefix of the filenames. An instance of the class BDD2Dot is used to save these files in dot format.
///
/// If the parameter a_counter_example is set to true, a so called counter example is printed to stderr each time an
/// expression is encountered that is neither a contradiction nor a tautology. A counter example is a valuation for which
/// the expression does not hold.
///
/// If the parameter a_witness is set to false, a so called witness is printed to stderr each time such an expression is
/// encountered. A witness is a valuation for which the expression holds.
///
/// The function Formula_Checker::check_formulas prints information to stderr indicating whether the expressions in the
/// list of formulas passed as parameter a_formulas are tautologies or contradictions. In some cases the BDD based prover
/// may be unable to determine whether an expression is a tautology or a contradiction. If this is the case, the function
/// Formula_Checker::check_formulas will print information to stderr indicating this fact.
class Formula_Checker
{
  private:
    /// \brief BDD based prover.
    mcrl2::data::detail::BDD_Prover f_bdd_prover;
 
    /// \brief Class that outputs BDDs in dot format.
    BDD2Dot f_bdd2dot;
 
    /// \brief Flag indicating whether or not counter-examples are displayed.
    bool f_counter_example;
 
    /// \brief Flag indicating whether or not witnesses are displayed.
    bool f_witness;
 
    /// \brief Prefix for the names of the files containing BDDs in dot format.
    std::string f_dot_file_name;
 
    /// \brief Displays a witness.
    void print_witness()
    {
      if (f_witness)
      {
        const data_expression v_witness = f_bdd_prover.get_witness();
        if (v_witness==data_expression())
        {
          throw mcrl2::runtime_error(
            "Cannot print witness. This is probably caused by an abrupt stop of the\n"
            "conversion from expression to EQ-BDD. This typically occurs when a time limit is set.\n"
          );
        }
        else
        {
          mCRL2log(log::log_level_t::info) << "  Witness: " << v_witness << std::endl;
        }
      }
    }
 
    /// \brief Displays a counter-example.
    void print_counter_example()
    {
      if (f_counter_example)
      {
        const data_expression v_counter_example = f_bdd_prover.get_counter_example();
        if (v_counter_example==data_expression())
        {
          throw mcrl2::runtime_error(
            "Cannot print counter example. This is probably caused by an abrupt stop of the\n"
            "conversion from expression to EQ-BDD. This typically occurs when a time limit is set.\n"
          );
        }
        else
        {
          mCRL2log(log::log_level_t::info) << "  Counter-example: " << v_counter_example << std::endl;
        }
      }
    }
 
    /// \brief Writes the BDD corresponding to the formula with number a_formula_number to a dot file.
    void save_dot_file(int a_formula_number)
    {
      if (!f_dot_file_name.empty())
      {
        f_bdd2dot.output_bdd(f_bdd_prover.get_bdd(), f_dot_file_name + "-" + std::to_string(a_formula_number) + ".dot");
      }
    }
 
  public:
    /// \brief Constructor that initializes Formula_Checker::f_counter_example, Formula_Checker::f_witness,
    /// \brief Formula_Checker::f_bdd_prover and Formula_Checker::f_dot_file_name.
    /// precondition: the argument passed as parameter a_time_limit is greater than or equal to 0. If the argument is equal
    /// to 0, no time limit will be enforced
    Formula_Checker(mcrl2::data::data_specification a_data_spec,
      mcrl2::data::rewriter::strategy a_rewrite_strategy = mcrl2::data::rewrite_strategy::jitty,
      int a_time_limit = 0,
      bool a_path_eliminator = false,
      mcrl2::data::detail::smt_solver_type a_solver_type = mcrl2::data::detail::smt_solver_type::solver_type_cvc,
      bool a_apply_induction = false,
      bool a_counter_example = false,
      bool a_witness = false,
      char const* a_dot_file_name = nullptr)
      : f_bdd_prover(a_data_spec,
          used_data_equation_selector(a_data_spec),
          a_rewrite_strategy,
          a_time_limit,
          a_path_eliminator,
          a_solver_type,
          a_apply_induction),
        f_dot_file_name(a_dot_file_name)
    {
      f_counter_example = a_counter_example;
      f_witness = a_witness;
    }
 
    /// \brief Destructor without any specific functionality.
    ~Formula_Checker() = default;
 
    /// \brief Checks the formulas in the list a_formulas.
    /// precondition: the parameter a_formulas is a list of expressions of sort Bool in internal mCRL2 format
    void check_formulas(const data_expression_list& a_formulas)
    {
      int v_formula_number = 1;
 
      for (const auto& v_formula: a_formulas)
      {
        mCRL2log(log::log_level_t::info) << "'" << v_formula << "'";
        f_bdd_prover.set_formula(v_formula);
        Answer v_is_tautology = f_bdd_prover.is_tautology();
        Answer v_is_contradiction = f_bdd_prover.is_contradiction();
        if (v_is_tautology == Answer::answer_yes)
        {
          mCRL2log(log::log_level_t::info) << "Tautology" << std::endl;
        }
        else if (v_is_contradiction == Answer::answer_yes)
        {
          mCRL2log(log::log_level_t::info) << "Contradiction" << std::endl;
        }
        else
        {
          mCRL2log(log::log_level_t::info) << "Undeterminable" << std::endl;
          print_counter_example();
          print_witness();
          save_dot_file(v_formula_number);
        }
        v_formula_number++;
      }
    }
 
};
 
} // namespace mcrl2::data::detail
 
#endif