# -*- coding: utf-8 -*-
## Filename    : CLUnfolder.py
## Author(s)   : Michel Le Borgne
## Created     : 22 mars 2012
## Revision    :
## Source      :
##
## Copyright 2012 : IRISA/IRSET
##
## This library is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published
## by the Free Software Foundation; either version 2.1 of the License, or
## any later version.
##
## This library is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY, WITHOUT EVEN THE IMPLIED WARRANTY OF
## MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  The software and
## documentation provided here under is on an "as is" basis, and IRISA has
## no obligations to provide maintenance, support, updates, enhancements
## or modifications.
## In no event shall IRISA be liable to any party for direct, indirect,
## special, incidental or consequential damages, including lost profits,
## arising out of the use of this software and its documentation, even if
## IRISA have been advised of the possibility of such damage.  See
## the GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this library; if not, write to the Free Software Foundation,
## Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
##
## The original code contained here was initially developed by:
##
##     Michel Le Borgne.
##     IRISA
##     Symbiose team
##     IRISA  Campus de Beaulieu
##     35042 RENNES Cedex, FRANCE
##
##
## Contributor(s): Geoffroy Andrieux IRSET
##
"""
Main engine for constraint unfolding and solving
"""
from __future__ import print_function

#from pyCryptoMS import CryptoMS
from pycryptosat import Solver as CryptoMS
from cadbiom.models.biosignal.translators.gt_visitors import compile_cond, compile_event
from cadbiom.models.clause_constraints.CLDynSys import Clause, Literal
from cadbiom.models.clause_constraints.mcl.MCLSolutions import RawSolution, MCLException
from cadbiom import commons as cm

# C++ API
from _cadbiom import shift_clause, shift_dynamic, forward_code, \
                     forward_init_dynamic

# Standard imports
from logging import DEBUG
import itertools as it

LOGGER = cm.logger()

class CLUnfolder(object):
    """
    When loading a model in a MCLAnalyser object, a CLUnfolder is generated which
    implies the compilation of the dynamical system into a clause constraint
    dynamical system and the DIMACS coding of all the variables.
    This coding cannot be changed later.
    The unfolding of constraints is performed efficiently on the numeric form
    of the clause constraints. The CLUnfolder provide various method to convert
    variable names to DIMACS code and back, to extract the frontier of a model
    and to extract informations from raw solutions.

    Dynamic constraints unfolding management
    ========================================
    Each variable is coded as an integer (in var_code_table and var_list).
    Each clause is represented as a list of signed integers (DIMACS coding).

    During unfolding, clauses are shifted either to the future (forward) or
    to the past (backward). The shift operator is a simple addition
    of self.__shift_step. The shift direction depends only on initializations.
    self.__shift_step depends on the number of variables so it is impossible
    to add variables while generating a trajectory unfolding.

    Glossary
    ========
    - ground variables/ground dimacs code: variables at time 0/their encoding.
    - solution: a solution of the logical dynamic constraint from SAT solver
    - state vector: list of DIMACS code of original (not shifted) variables
      corresponding to a step.
    - trajectory: list of state_vectors
    """

    def __init__(self, dynamic_system):
        """
        :param dynamic_system: Describe a dynamic system in clause form.
        :type dynamic_system: <CLDynSys>
        """
        self.dynamic_system = dynamic_system # symbolic clause dynamic system

        # shift_step equals to the total number of coded variables
        # (including inputs, entities, clocks/events, auxiliary variables)
        # shift_step_init: the shift step ss (if n is X_0 code, n+ss is X_1 code)
        self.shift_step_init = dynamic_system.get_var_number() # shift step of system (number of variables of the system)
        self.__shift_step = self.shift_step_init  # current shift/step

        # self.shift_step must be frozen in order to avoid problems during the
        # unflatten() step of RawSolutions.
        # => Each step MUST have the same number of variables.
        # Thus, we lock the Unfolder by turning self.__locked to True.
        # See __shift_clause() and __m_shift_clause()
        self.__locked = False
        self.__current_step = 1                   # current number of unfolding
        # For reachability optimisation. Number of shifts before checking
        # the final property
        self.__steps_before_check = 0

        # assign a DIMACS code number to each variable (invariant)
        # Create mappings between names and values of the variables of the system
        # dynamic_system.base_var_set : Set of ALL variables of the dynamic system
        # (including inputs, entities, clocks/events, auxiliary variables).
        self.__var_code_table = dict()     # Mapping: name -> DIMACS code (!= 0)
        self.__var_list = ['##']           # Mapping: DIMACS code (!= 0) -> name

        # Fix order of variables names with a list:
        # - indexes of __var_list are the values of the variables at these indexes
        # - values begin from 1 (0 is a blacklisted value)
        base_var_set = list(dynamic_system.base_var_set)
        self.__var_list += base_var_set
        # keys: are the names of the variables, values: their values
        self.__var_code_table = \
            {var_name: var_num for var_num, var_name in enumerate(base_var_set, 1)}
        # Optimization: for forward_init_dynamic() and forward_code() (mostly
        # implemented in C.
        # Precompute __var_code_table with the literal names in "future" format;
        # i.e with a last char '`' at the end.
        # Thus it is easy to search them directly in the dict (in O(1)),
        # instead of slicing them.
        # Note: "future" literals are already in self.dynamic_system.list_clauses
        # and maybe in self.dynamic_system.aux_list_clauses
        temp_var_code_table = \
            {var_name + "`": var_num for var_name, var_num in self.__var_code_table.iteritems()}
        self.__var_code_table.update(temp_var_code_table)

        assert len(self.__var_code_table) == 2 * self.__shift_step

        # Include auxiliary clause to eliminate undesirable solutions
        # If A->B has clock h, an aux constraint added is h included in h when A
        # Must be set to False for inhibitors computations
        self.__include_aux_clauses = True
        self.__lit_cpt = self.__shift_step + 1    # counter for aux. var. coding

        # Same mapping tools for auxiliary variables introduced by properties
        # compilation
        # Cf __code_clause()
        self.__aux_code_table = dict()            # name to code
        self.__aux_list = []                      # code to name

        # ordered list of DIMACS codes of the simple variables/places
        # Disable all variables of places (entities) in the model (except frontiers)
        self.__no_frontier_init = [[-self.__var_code_table[nfp]] for nfp in self.dynamic_system.no_frontiers]

        # ordered list of DIMACS codes of the frontier variables/places
        self.frontier_values = [self.__var_code_table[frp] for frp in self.dynamic_system.frontiers]
        self.frontier_values.sort()
        ## TODO: sort utile ici ???? si non passer en frozenset et supprimer les casts partout ailleurs
        ## Cf RawSolution.frontier_pos_and_neg_values BACKWARD, encore utilisé avec index
        ## Cf TestCLUnfolder.test_frontier indexable mais peut etre contourné

        # Precompute convenient attributes for:
        # frontiers_pos_and_neg:
        #     - RawSolution.frontier_pos_and_neg_values
        #     (set operation with solution variables)
        # frontiers_negative_values:
        #     - MCLQuery.from_frontier_sol_new_timing
        #     - MCLQuery.frontiers_negative_values
        #     - MCLAnalyser.__solve_with_inact_fsolution
        #     - TestCLUnfolder.test_prune
        #
        # Set of frontier positive and negative values
        # (all frontiers and their opposite version).
        # => operations with sets are much faster
        self.frontiers_negative_values = \
            frozenset(-frontier for frontier in self.frontier_values)
        self.frontiers_pos_and_neg = \
            self.frontiers_negative_values | frozenset(self.frontier_values)

        # DIMACS codes of the input variables/places for extraction (inv)
        self.__inputs = frozenset(self.__var_code_table[inp] for inp in self.dynamic_system.inputs)

        # DIMACS codes of the free_clocks variables/places for extraction (invariant)
        self.__free_clocks = frozenset(self.__var_code_table[fcl] for fcl in self.dynamic_system.free_clocks)

        # Binding for a merged version of __inputs and __free_clocks
        # Convenient attribute for RawSolution.extract_act_input_clock_seq()
        # DIMACS codes of the input and free_clocks variables
        self.inputs_and_free_clocks = self.__inputs | self.__free_clocks

        # Properties to be checked
        self.reset()

        # Logical constraints:
        # Result from unfolding of base constraints
        # Boolean vectors signification:
        # X: Current state of places (activated/unactivated)
        # X': Future state of places
        # H: Current 'free' events (present/not present) => ?
        # I: Current inputs => ?
        self.__dynamic_constraints = []        # DIMACS clauses: X' = f(X,H,I)

        # Simple temporal properties:
        # SP(X0): Initial property/start property; Never change at each step.
        # IP(X): Invariant property
        # VP(X): Variant property
        #   List of logical formulas of properties forced at each step
        #   It's the trajectory of events of a solution.
        # FP(X): Final property

        self.__initial_constraints = []        # DIMACS clauses: C(X_0) <list <list <int>>>
        self.__final_constraints   = []        # idem: C(X_n)
        self.__invariant_constraints = []      # DIMACS clauses: C(X_i))
        self.__variant_constraints = []        # variant constraints along trajectory
        self.__shift_direction = None          # FORWARD or BACKWARD

        # statistics on solver
        self.__stats = False
        self.__nb_vars = 0
        self.__nb_clauses = 0


    def reset(self):
        """Reset the unfolder before a new query

        Reset only properties and dimacs clauses from the current query;
        AND __list_variant_constraints.

        This function is called from the constructor and during
        MCLAnalyser.sq_is_satisfiable() and MCLAnalyser.sq_solutions()
        following the call of init_with_query().
        """
        # Properties to be checked
        self.__initial_property = None            # logical formula - literal boolean expression
        self.__dimacs_initial = None              # list of DIMACS clauses
        self.__final_property = None              # logical formula
        self.__dimacs_final = None                # list of DIMACS clauses
        self.__invariant_property = None          # logical formula
        self.__dimacs_invariant = None            # list of DIMACS clauses
        self.__variant_property = None            # list<logic formulas>
        self.__dimacs_variant = None              # list<list<DIMACS clauses>>
        # list of variant temporal constraints in Dimacs ground code
        self.__list_variant_constraints = None    # list<list<DIMACS clauses>>

        # If this function is called from the constructor,
        # the following variables are just redefined here.

        # For reachability optimisation. Number of shifts before checking
        # the final property
        self.__steps_before_check = 0
        self.__shift_direction = None             # FORWARD or BACKWARD
        self.__locked = False

    def init_with_query(self, query):
        """Initialise the unfolder with the given query

        Following attributes are used from the query:
            start_prop, dim_start, inv_prop, dim_inv, final_prop, dim_final,
            variant_prop, dim_variant_prop, steps_before_check

        Textual properties of query are compiled into numeric clauses in
        init_forward_unfolding(), just before squery_is_satisfied() and
        squery_solve().
        This compilation step is costly due to ANTLR performances...
        """
        # Reset the unfolder before a new query
        self.reset()
        # Init with query properties and clauses
        self.__initial_property = query.start_prop # logical formula in text
        self.__dimacs_initial = query.dim_start

        self.__final_property = query.final_prop # logical formula in text
        self.__dimacs_final = query.dim_final

        self.__invariant_property = query.inv_prop # logical formula in text
        self.__dimacs_invariant = query.dim_inv

        # It's the trajectory of events of a solution.
        self.__variant_property = query.variant_prop # logical formula in text
        self.__dimacs_variant = query.dim_variant_prop

        # For reachability optimisation. Number of shifts before checking
        # the final property (default 0)
        self.__steps_before_check = query.steps_before_check

    def set_stats(self):
        """Enable solver statistics (for tests)"""
        self.__stats = True
        self.__nb_vars = 0
        self.__nb_clauses = 0

    def unset_stats(self):
        """Disable solver statistics (never used)"""
        self.__stats = False

    def _stats(self):
        """Display solver statistics"""
        print("\n NB Variables in solver:", self.__nb_vars)
        print("NB Clauses in solver:", self.__nb_clauses)

    def set_include_aux_clauses(self, val):
        """
        Include auxiliary clause to eliminate undesirable solutions
        If A->B has clock h, an aux constraint added is h included in h when A
        Must be set to False for inhibitors computations
        """
        self.__include_aux_clauses = val

    ## Internal variable access for tests (never used) #########################
    @property
    def dynamic_constraints(self):
        """For tests: returns coded dynamic constraints"""
        return self.__dynamic_constraints

    @property
    def initial_constraints(self):
        """For tests: returns coded initial constraints"""
        return self.__initial_constraints

    @property
    def invariant_constraints(self):
        """For tests: returns coded invariant constraints"""
        return self.__invariant_constraints

    @property
    def variant_constraints(self):
        """For tests: returns coded variant constraints"""
        return self.__variant_constraints

    @property
    def final_constraints(self):
        """For tests: returns coded final constraints"""
        self.__final_constraints

    ## Variables management ####################################################
    def var_names_in_clause(self, clause):
        """Return the names of the variables from values in the given numeric clause
        (DEBUG never used)
        """
        return [self.get_var_indexed_name(var) for var in clause]

    def var_dimacs_code(self, var_name):
        """Returns DIMACS code of var_name (string) variable (for tests)"""
        return self.__var_code_table[var_name]

    def get_system_var_number(self):
        """Get number of variables in the clause constraint dynamical system
        (including inputs, entities, clocks/events, auxiliary variables) (for tests)

        .. note:: This number should be equal to the number of variables
            in self.get_var_number()
        """
        return self.dynamic_system.get_var_number()

    def get_var_number(self):
        """Get number of principal variables (properties excluded) in the unfolder
        (including inputs, entities, clocks/events, auxiliary variables) (for tests)

        .. note:: This number should be equal to the number of variables
            in self.get_system_var_number()
        """
        # Remove the blacklisted first item (##) for variables naming
        return len(self.__var_list) - 1

    def get_var_name(self, var_num):
        """Get name of the variable

        .. seealso:: Explanations on get_var_indexed_name()

        @param var_num: DIMACS literal coding of an initial variable
        @return: name of the variable
        """
        # Get the original var_code without shifts
        var_code = (abs(var_num) - 1) % self.__shift_step + 1
        if var_code <= self.shift_step_init:
            # Variable num is less than the number of the variables in the system
            # => variable from the initial system
            return self.__var_list[var_code]
        else:
            # auxiliary variable introduced by properties compilation
            return self.__aux_list[var_code - self.shift_step_init -1]
            #raise MCLException("Not a DIMACS code of an initial variable")

    def get_var_indexed_name(self, var_num):
        """Get name of the variable with the time index appended

        .. note:: time index is the number of steps since the begining of the
            simulation.

            :Example:
                __shift_step = 2 (current step of the unfolding)
                shift_step_init = 2 (number of variables in the system)
                __var_list = ["##", "n1", "n2"]

                Virtual list of indexes in the state vector of a solution:
                [0, 1, 2, 3, 4, 5, 6, 7, 8, ...]
                 #|n1,n2|n1,n2|n1,n2|n1,n2|
                   ti=0  ti=1  ti=2  ti=3

                Given var_num = 7:
                index of var_name in __var_list: ((7-1) % 2) + 1 = 1
                var_name = "n1"
                time index: (7 - 1) / 2 = 3

                => return: "n1_3"

        @param var_num: DIMACS literal coding
        @return: name of the variable with the time index appended
        """
        varnum1 = abs(var_num)
        # Get the original var_code without shifts
        var_code = (varnum1 - 1) % self.__shift_step + 1
        var_step = (varnum1 - var_code) / self.__shift_step
        if var_code <= self.shift_step_init:
            # Variable num is less than the number of the variables in the system
            # => variable from the initial system
            return self.__var_list[var_code] + '_%s'% var_step
        else:
            # Auxiliary variable introduced by properties compilation
            index = var_code - self.shift_step_init - 1
            return self.__aux_list[index] + '_%s'% var_step

    def get_free_clocks(self):
        """Get the DIMACS codes of the free_clocks variables"""
        return self.__free_clocks

    def get_inputs(self):
        """Get the DIMACS codes of the input variables"""
        return self.__inputs

    def get_shift_direction(self):
        """
        @return: string "FORWARD" or "BACKWARD"
        """
        return self.__shift_direction

    def get_shift_step(self):
        """
        @return: the shift step ss (if n is X_0 code, n+ss is X_1 code)
        """
        return self.__shift_step

    def get_current_step(self):
        """
        @return: the current number of unfolding
        """
        return self.__current_step


    ## Translation from names to num codes #####################################
    ## The translation depends on the shift direction
    def __forward_code(self, clause):
        """(deprecated, directly included in C++ module: forward_init_dynamic())

        Numerically code a clause with the numeric code found in
        self.__var_code_table for a base variable x,
        and numeric_code + shift_step for x' variable

        ..note:: Future variables x' are noted "name`" in Literal names.
            Values of variables increases of __shift_step in future steps.

        @param clause: a Clause object
        @return: the DIMACS coding of the forward shifted clause
        """
        # Old API
        # num_clause = []
        # for lit in clause.literals:
        #     if lit.name[-1] == '`': # t+1 variable
        #         num_clause.append(
        #             -(self.__var_code_table[lit.name[:-1]] + self.__shift_step) \
        #             if not lit.sign \
        #             else (self.__var_code_table[lit.name[:-1]] + self.__shift_step)
        #         )
        #     else: # t variable
        #         num_clause.append(
        #             -self.__var_code_table[lit.name] \
        #             if not lit.sign else self.__var_code_table[lit.name]
        #         )
        # return num_clause

        # New API via C++ module
        return forward_code(clause, self.__var_code_table, self.__shift_step)


    def __backward_code(self, clause):
        """(never used, backward is partially implemented)

        numerically code a clause with the numeric code found in
        self.__var_code_table + shift_step for a base variable x,
        and numeric_code for x' variable integer coding increases in past steps

        @param clause: a Clause object
        @return: the DIMACS coding of the backward shifted clause
        """
        num_clause = []
        for lit in clause.literals:
            if lit.name[-1] == '`': # t+1 variable
                num_clause.append(
                    -self.__var_code_table[lit.name[:-1]] \
                    if not lit.sign \
                    else self.__var_code_table[lit.name[:-1]]
                )
            else: # t variable, base variable
                num_clause.append(
                    -(self.__var_code_table[lit.name] + self.__shift_step) \
                    if not lit.sign \
                    else (self.__var_code_table[lit.name] + self.__shift_step)
                )
        return num_clause

    def __code_clause(self, clause):
        """Numerically code a clause

        The numerical values are found in
        self.__var_code_table for variables in the dynamic system,
        or in self.__aux_code_table for other auxiliary variables;
        assume all variables are basic variables (t=0)

        @warning: MODIFIES SHIFT_STEP if auxiliary variables are present (numeric code)
            Because we add a variable in the system...

        :param clause:
        :return: List of numerical values corresponding to the literals
            in the given clause.
        :type clause: <Clause>
        :rtype: <list <int>>
        """
        num_clause = []
        for lit in clause.literals:
            # Get variable value with the given name
            name = lit.name
            if name in self.__var_code_table:
                var_cod = self.__var_code_table[name]
            elif name in self.__aux_code_table:
                var_cod = self.__aux_code_table[name]
            else:
                # Create an auxiliary variable - modifies shift_step (nb of variables)
                self.__shift_step += 1
                # Mapping name to value code
                self.__aux_code_table[name] = self.__shift_step
                # Mapping value code to name
                self.__aux_list.append(name)
                var_cod = self.__shift_step

            # Add the sign to the value
            lit_code = var_cod if lit.sign else -var_cod

            num_clause.append(lit_code)
        return num_clause

    ## Dynamic initialisations #################################################
    def __forward_init_dynamic(self):
        """Dynamics initialisations.
        Set dynamic constraints for a forward one step: X1 = f(X0)

        Numerically code clauses with the numeric codes found in
        self.__var_code_table for a base variable x,
        and numeric_code + shift_step for x' variable integer coding increases
        in future steps.

        __dynamic_constraints is a list of lists of numeric clauses (lists of ints)
        Each sublist of __dynamic_constraints corresponds to a step in the unfolder;
        the last step is the last element.

        .. note:: Called by init_forward_unfolding()

        .. note:: Future variables x' are noted "name`" in Literal names.

        .. note:: Values of variables increases of __shift_step in future steps.
        """
        # New API via C++ module
        # TODO: take a look at __backward_init_dynamic & __backward_code
        if self.__include_aux_clauses:
            # Auxiliary clauses are supported (default)
            self.__dynamic_constraints = \
                forward_init_dynamic(self.dynamic_system.list_clauses,
                                     self.__var_code_table,
                                     self.__shift_step,
                                     self.dynamic_system.aux_list_clauses)
        else:
            self.__dynamic_constraints = \
                forward_init_dynamic(self.dynamic_system.list_clauses,
                                     self.__var_code_table,
                                     self.__shift_step)

    def __backward_init_dynamic(self):
        """Dynamics initialisations. (never used, backward is partially implemented)
        Set dynamic constraints for a forward one step: X0 = f(X1)

        .. note:: Called by init_backward_unfolding()
        """
        num_clause_list = \
            [self.__backward_code(clause)
             for clause in self.dynamic_system.list_clauses]

        if self.__include_aux_clauses:
            num_clause_list += \
                [self.__backward_code(clause)
                 for clause in self.dynamic_system.aux_list_clauses]

        self.__dynamic_constraints = [num_clause_list]

    ## Shifting variables: implementation of the shift operator ################
    def __shift_clause(self, ncl):
        """Shift a clause for the current __shift_step

        (no used anymore, replaced by direct use of C++ code)

        Basically, `shift_step` is added to positive variables and subtracted
        from negative variables in `numeric_clause`.

        self.shift_step must be frozen in order to avoid problems during the
        unflatten() step of RawSolutions.
        => Each step MUST have the same number of variables.
        Thus, we lock the Unfolder by turning self.__locked to True.

        @param ncl: DIMACS clause ## TODO rename
        @warning: lock the unfolder
        """
        # Froze unfolder to avoid modifications of shift_step
        self.__locked = True

        # Old API
        # Less efficient with abs()
        # return [(abs(lit) + self.__shift_step) * (-1 if lit < 0 else 1) for lit in ncl]
        # More efficient with ternary assignment
        # return [(lit + self.__shift_step) if lit > 0 else (lit - self.__shift_step)
        #         for lit in ncl]

        # New API via C++ module
        return shift_clause(ncl, self.__shift_step)

    def __m_shift_clause(self, ncl, nb_steps):
        """Shift a clause for the given step number

        self.shift_step must be frozen in order to avoid problems during the
        unflatten() step of RawSolutions.
        => Each step MUST have the same number of variables.
        Thus, we lock the Unfolder by turning self.__locked to True.

        Called by: __shift_variant()


        @param ncl: DIMACS clause
        @param nb_steps: number of shifts asked
        @warning: lock the unfolder
        """
        # Froze unfolder to avoid modifications of shift_step
        self.__locked = True

        return [(lit + self.__shift_step * nb_steps) if lit > 0
                else (lit - self.__shift_step * nb_steps) for lit in ncl]

    def __shift_dynamic(self):
        """Shift clauses representing the dynamics X' = f(X,I,C)

        Shift the last item of self.__dynamic_constraints and append the result
        to self.__dynamic_constraints.

        .. note:: Called by shift()
        """
        # Old API
        # self.__dynamic_constraints.append(
        #   [self.__shift_clause(clause)
        #    for clause in self.__dynamic_constraints[-1]]
        # )

        # New API via C++ module
        # __dynamic_constraints:
        # List of lists of DIMACS encoded clauses (lists of ints)
        self.__dynamic_constraints.append(
            shift_dynamic(
                self.__dynamic_constraints[-1], # <list <list <int>>>
                self.__shift_step
            )
        )

    def __shift_initial(self):
        """Shift initialisation condition

        .. note:: Called by:
            - shift()
            - init_backward_unfolding()
        """
        self.__initial_constraints = \
            shift_dynamic(
                self.__initial_constraints,
                self.__shift_step
            )

    def __shift_final(self):
        """Shift final property

        .. note:: Called by:
            - shift()
            - init_forward_unfolding()
        """
        self.__final_constraints = \
            shift_dynamic(
                self.__final_constraints,
                self.__shift_step
            )

    def __shift_invariant(self):
        """Shift invariant property

        .. note:: Called by:
            - shift()
            - init_forward_unfolding()
            - init_backward_unfolding()
        """
        if self.__invariant_constraints:
            # New API via C++ module
            self.__invariant_constraints.append(
                shift_dynamic(
                    self.__invariant_constraints[-1],
                    self.__shift_step
                )
            )

    def __shift_variant(self):
        """Shift variant property - depends on unfolding direction

        ## TODO audit...

        .. warning:: Refactor note: unclear function. No apparent reason for
            only the first clause to be shifted...

        Process:
            - Take the clauses (constraint) of the current step
            - Shift the first clause
            - Append it to __variant_constraints
            - Stop ????

            Example:
            current_step: 2 (shift for step 3)
            [[], [[4], [4]], [[6], [7]], []]
            => Only [6] is shifted...

        .. note:: Called by shift()
        """
        if not self.__list_variant_constraints:
            return
        if self.__shift_direction == "FORWARD":
            # Constraint t0 already included from the query during initialisation
            current_constraint = self.__list_variant_constraints[self.__current_step]
            # shift constraint at current step and add to var_constraints
            for clause in current_constraint:
                s_clause = self.__m_shift_clause(clause, self.__current_step)
                self.__variant_constraints.append(s_clause)
                return # ?????
        elif self.__shift_direction == "BACKWARD":
            raise MCLException("Not yet implemented")
        else:
            raise MCLException("Shift incoherent data: " + self.__shift_direction)


    def shift(self):
        """Shift all clauses of one step

        self.__current_step is incremented here!

        Clauses shifted:
            - __dynamic_constraints[-1] (last element)
            - __invariant_constraints[-1] (last element)
            - __list_variant_constraints => TODO: audit...
            - __final_constraints if __shift_direction is "FORWARD"
            - __initial_constraints if __shift_direction is "BACKWARD"
        """
        # Froze unfolder to avoid modifications of shift_step
        self.__locked = True

        self.__shift_dynamic()
        self.__shift_invariant()
        self.__shift_variant()
        if self.__shift_direction == 'FORWARD':
            self.__shift_final()
        elif self.__shift_direction == 'BACKWARD':
            self.__shift_initial()
        else:
            # Shift direction must be set
            raise MCLException("Shift incoherent data: " + self.__shift_direction)

        # Increment the current step
        self.__current_step += 1

    ## Coding of properties ####################################################
    def __compile_property(self, property_text):
        """Compile a property (logical formula) into clauses

        Type checking uses the symbol table of dyn_sys
        Error reporting is made through the dyn_sys reporter

        .. warning:: MODIFIES __lit_cpt for numbering of auxiliary variables (not coding)

        .. note:: Called by:
            - __init_initial_constraint_0()
            - __init_final_constraint_0()
            - __init_invariant_constraint_0()
        """
        if self.__locked:
            raise MCLException("Trying to compile property while unfolder is locked")

        # syntax analyser and type checker
        # property_text, symb_t, reporter
        tree_prop = compile_cond(property_text,
                                 self.__dyn_sys.symb_tab,
                                 self.__dyn_sys.report)
        # avoid name collisions of aux var
        prop_visitor = CLPropertyVisitor(self.__lit_cpt)
        tree_prop.accept(prop_visitor)
        self.__lit_cpt = prop_visitor.cpt # avoid name collisions of aux var
        return prop_visitor.clauses

    def __compile_event(self, property_text):
        """Compile an event (biosignal expression) into clauses

        Type checking uses the symbol table of dyn_sys
        Error reporting is made through the dyn_sys reporter

        .. warning:: MODIFIES __lit_cpt for numbering of auxiliary variables (not coding)

        .. note:: Called by:
            - __init_variant_constraints_0()
        """
        if self.__locked:
            raise MCLException("Trying to compile property while unfolder is locked")

        # Syntax analyser and type checker
        tree_prop, ste, fcl = compile_event(
            property_text,
            self.dynamic_system.symb_tab,
            True,
            self.dynamic_system.report
        )
        # Avoid name collisions of aux var
        prop_visitor = CLPropertyVisitor(self.__lit_cpt)
        tree_prop.accept(prop_visitor)
        self.__lit_cpt = prop_visitor.cpt # avoid name collisions of aux var
        return prop_visitor.clauses

    def __init_initial_constraint_0(self, no_frontier_init=True):
        """
        if initial property is set, generate constraints clauses in numeric form
        base variable form - we have to wait until all variables are num coded
        before shifting anything!!
        """
# OLD
#        self.__initial_constraints = []
#        if no_frontier_init:
#            # initialize no frontier places to False
#            for nfp in self.__no_frontier_init:
#                self.__initial_constraints.append(nfp)
#        if self.__initial_property:
#            # compile initial property
#            l_clauses = self.__compile_property(self.__initial_property)
#            # compile numeric form
#            for clause in l_clauses:
#                self.__initial_constraints.append(self.__code_clause(clause))
#        # dimacs aux initial properties
#        dim_init = self.__dim_initial
#        if dim_init:
#            self.__initial_constraints = self.__initial_constraints + dim_init

        self.__initial_constraints = list()

        # initialize no frontier places to False
        if no_frontier_init:
            self.__initial_constraints += [elem for elem in self.__no_frontier_init]

        if self.__initial_property:
            # compile initial property
            # compile numeric form
            self.__initial_constraints += [self.__code_clause(clause) for clause in self.__compile_property(self.__initial_property)]

        # dimacs aux initial properties
        if self.__dim_initial:
            self.__initial_constraints += self.__dim_initial

    def __init_final_constraint_0(self):
        """
        if final property is set, generate constraints clauses in numeric form
        base variable used - we have to wait until all variables are num coded
        before shifting anything!!
        """

        self.__final_constraints = []
        if self.__final_property:
            # compile initial (X0) property
            # ex: Px => [$Px$]
            l_clauses = self.__compile_property(self.__final_property)
            # compile numeric form
            # ex: [$Px$] => self.__final_constraints = [[7]]
            for clause in l_clauses:
                self.__final_constraints.append(self.__code_clause(clause))
        dim_fin = self.__dim_final
        if dim_fin:
            self.__final_constraints = self.__final_constraints + dim_fin

    def __init_invariant_constraint_0(self):
        """
        if trajectory property is set, generate constraints clauses in numeric form
        base variable used - we have to wait until all variables are num coded
        before shifting anything!!
        """
        self.__invariant_constraints = []
        if self.__invariant_property:
            # compile initial (X0) property
            l_clauses = self.__compile_property(self.__invariant_property)
            # compile numeric form
            init_const = []
            for clause in l_clauses:
                init_const.append(self.__code_clause(clause))
            self.__invariant_constraints.append(init_const)
        d_inv = self.__dim_invariant
        if d_inv:
            self.__invariant_constraints = self.__invariant_constraints + d_inv

    def __init_variant_constraints_0(self):
        """Code variant constraints in a numerical clause.

        variant_property list d'étapes, chaque étape a une formule logique impliquant les évènements (et les places? pas sur.;)
        => ensemble de place/propriétés devant ^etre valides à chaque étape

        If variant_property is set, compile each property into clauses and
        encode these clauses. Clauses already in dimacs form are added.
        The two variant constraint forms must be compatible (same length)

        self.__list_variant_constraints is built here and is used later to shift
        given variant properties in __shift_variant().
        """
        # coding of variant properties
        # Take __variant_property in priority on __dimacs_variant
        if self.__variant_property:
            self.__list_variant_constraints = list()

            for prop in self.__variant_property:
                # compile initial (X0) property into numeric form
                # For each property in step of __variant_property
                self.__list_variant_constraints.append(
                    [self.__code_clause(clause)
                     for clause in self.__compile_event(prop)]
                )
                print(self.__list_variant_constraints)

            if self.__dimacs_variant:
                # Add DIMACS aux clauses initial properties
                # Check if the number of steps is equal
                if len(self.__variant_property) != len(self.__dimacs_variant):
                    raise MCLException(
                        "Incoherent variant properties; sizes of "
                        "__variant_property and __dimacs_variant differ"
                    )

                # Merge together all steps content
                # Ex:
                # __list_variant_constraints due to __variant_property convertion:
                # [[], [[4]], [], []]
                # __dimacs_variant:
                # [[], [[4]], [[6], [7]], []]
                # Result:
                # [[], [[4], [4]], [[6], [7]], []]
                self.__list_variant_constraints = \
                    [list(it.chain(*cpl)) for cpl
                     in zip(self.__dimacs_variant, self.__list_variant_constraints)]

        elif self.__dimacs_variant:
            # No __variant_property, keep only __dimacs_variant
            self.__list_variant_constraints = self.__dimacs_variant

        # Initialisation
        if self.__list_variant_constraints:
            if self.__shift_direction == "FORWARD":
                # For now, keep only the events of the first step (t0)
                # Other steps are taken during shift() calls
                self.__variant_constraints = self.__list_variant_constraints[0]
            elif  self.__shift_direction == "BACKWARD":
                raise MCLException("Not yet implemented")
            else:
                raise MCLException("Shift incoherent data: " + self.__shift_direction)

    ## Whole initialisations ###################################################
    def init_forward_unfolding(self):
        """Initialisation before generating constraints - forward trajectory

        Called at the begining of squery_is_satisfied() and squery_solve()
        """
        self.__shift_direction = 'FORWARD'
        self.__current_step = 1
        self.__shift_step = self.shift_step_init  # back to basic!
        self.__aux_code_table = dict()            # flush auxiliary variables
        self.__aux_list = []                      # idem

        # init properties to generate all variable num codes
        self.__init_initial_constraint_0()
        self.__init_final_constraint_0()
        self.__init_invariant_constraint_0()
        self.__init_variant_constraints_0()

        # now shifting is possible
        self.__forward_init_dynamic()
        self.__shift_final()
        self.__shift_invariant()


    def init_backward_unfolding(self):
        """Initialisation before generating constraints - backward trajectory
        Never used (and backward not implemented in __init_variant_constraints_0)
        """
        self.__shift_direction = 'BACKWARD'
        self.__current_step = 0
        self.__shift_step = self.shift_step_init  # back to basic!
        self.__aux_code_table = dict()            # flush auxiliary variables
        self.__aux_list = []                      # idem

        # init properties to generate all variable num codes
        self.__init_initial_constraint_0()
        self.__init_final_constraint_0()
        self.__init_invariant_constraint_0()
        self.__init_variant_constraints_0()

        # now shifting is possible
        self.__backward_init_dynamic()
        self.__shift_initial()
        self.__shift_invariant()

    ## Solver interface ########################################################
    def __load_solver(self, solv):
        """Add all the current clauses in the solver

        .. note:: Called by:
            - __constraints_satisfied()
            - __msolve_constraints()
        """
        # New API via C++ module
        solv.add_clauses(self.__final_constraints)
        solv.add_clauses(it.chain(*self.__invariant_constraints))
        solv.add_clauses(self.__variant_constraints)
        solv.add_clauses(it.chain(*self.__dynamic_constraints))
        solv.add_clauses(self.__initial_constraints)

        # LOGGING
        if LOGGER.getEffectiveLevel() == DEBUG:
            # final
            LOGGER.debug("Load new solver !!")
            LOGGER.debug(">> final constraints: %s", len(self.__final_constraints))
            LOGGER.debug(str(self.__final_constraints))

            # trajectory invariant
            LOGGER.debug(">> trajectory invariant constraints: %s", len(self.__invariant_constraints))
            LOGGER.debug(str(self.__invariant_constraints))

            # trajectory variant
            LOGGER.debug(">> trajectory variant constraints: %s", len(self.__variant_constraints))
            LOGGER.debug(str(self.__variant_constraints))

            # dynamics
            LOGGER.debug(">> dynamic constraints: %s", len(self.__dynamic_constraints))
            LOGGER.debug(str(self.__dynamic_constraints))

            # initial
            LOGGER.debug(">> initial constraints: %s", len(self.__initial_constraints))
            LOGGER.debug(str(self.__initial_constraints))


    def __constraints_satisfied(self):
        """Ask the SAT solver if the query/system is satisfiable in the given
        number of steps.

        .. warning:: vvars (frontier values) are not tested. Thus the satisfiability
            is not tested for interesting variables like in squery_solve().

        :return: True if the problem is satisfiable, False otherwise.
        :rtype: <boolean>
        """
        solver = CryptoMS()
        # Load all clauses into the solver
        self.__load_solver(solver)

        if self.__stats:
            # If stats are activated (never besides in test environment):
            # sync local data (nb vars, nb clauses with solver state)
            if solver.nb_vars() > self.__nb_vars:
                self.__nb_vars = solver.nb_vars()

            # Starting from pycryptosat 5.2, nb_clauses() is a private attribute
            #if solver.nb_clauses() > self.__nb_clauses:
            #    self.__nb_clauses = solver.nb_clauses()
        # Is the problem satisfiable ?
        return solver.is_satisfiable()


    def __msolve_constraints(self, max_sol, vvars):
        """Get solutions from the solver

        :param max_sol: The maximum number of solutions to be returned
        :param vvars: Variables for which solutions must differ.
            In practice, it is a list with the values (Dimacs code)
            of all frontier places of the system.
        :type max_sol: <int>
        :type vvars: <list <int>>
        :return: A tuple of RawSolution objects
            RawSolution objects contain a solution got from SAT solver with all
            variable parameters from the unfolder
        :rtype: <tuple <RawSolution>>
        """
        solver = CryptoMS()
        # Load all clauses into the solver
        self.__load_solver(solver)

        if self.__stats:
            # If stats are activated (never besides in test environment):
            # sync local data (nb vars, nb clauses with solver state)
            if solver.nb_vars() > self.__nb_vars:
                self.__nb_vars = solver.nb_vars()
            # Starting from pycryptosat 5.2, nb_clauses() is a private attribute
            #if solver.nb_clauses() > self.__nb_clauses:
            #    self.__nb_clauses = solver.nb_clauses()

        if LOGGER.getEffectiveLevel() == DEBUG:
            LOGGER.debug("__msolve_constraints :: vvars : %s", vvars)
            LOGGER.debug("__msolve_constraints :: max_sol : %s", max_sol)
            # Get List of solutions (list of tuples of literals)
            lintsol = solver.msolve_selected(max_sol, vvars)
            LOGGER.debug("__msolve_constraints :: lintsol : %s", lintsol)
            # Make a RawSolution for each solution (tuple of literals)
            return [RawSolution(solint, self) for solint in lintsol]

        return tuple(RawSolution(solint, self)
                for solint in solver.msolve_selected(max_sol, vvars))

    def squery_is_satisfied(self, max_step):
        """Ask the SAT solver if the query/system is satisfiable in the given
        number of steps.

        If __invariant_property is set and __final_property is not set,
        1 satisfiability test is made only after all shift() calls for each
        remaining step from the current step.

        Otherwise, 1 test is made for each remaining step after each shift() call.

        .. warning:: vvars (frontier values) are not tested. Thus the satisfiability
            is not tested for interesting variables like in squery_solve().

        :param max_step: The horizon on which the properties must be satisfied.
        :type max_step: <int>
        """
        # Initialization
        self.init_forward_unfolding()
        # Horizon adjustment
        if self.__list_variant_constraints:
            max_step = min(max_step, len(self.__list_variant_constraints)-1) ## TODO:  -1 ?

        if self.__invariant_property and not self.__final_property:
            # 1 satisfiability test is made only after all shift() calls for each step
            # Shift all remaining steps
            while self.__current_step <= max_step:
                self.shift()
            return self.__constraints_satisfied()

        else:
            # 1 test is made for each remaining step after each shift()

            # Check and correct for incoherent data on step number
            # __steps_before_check can't be >= max_step, otherwise
            # __current_step could be > max_step due to shift() of "auto shift loop"
            # and this function will not search any solution,
            # and will return an empty list.
            if self.__steps_before_check >= max_step:
                self.__steps_before_check = max_step - 1

            # Auto shift loop: Shift without checking (optimization)
            # Do not search solutions before the specified limit
            while self.__current_step < self.__steps_before_check:
                print("SATIS TEST AUTO SHIFT opti")
                self.shift()

            satisfiability_test = False

            while self.__current_step < max_step:
                # Shift the system
                self.shift()

                # Test satisfiability
                satisfiability_test = self.__constraints_satisfied()
                print("SATIS TEST done, current_step", self.__current_step)

                if satisfiability_test:
                    return True

            # Return the satisfiability status in all cases
            return satisfiability_test

    def squery_solve(self, vvars, max_step, max_sol):
        """Search max_sol number of solutions with max_step steps, involving vvars
        (frontiers) variables of interest.

        Assert a query is loaded (start_condition, inv_condition, final_condition)

        If __invariant_property is set and __final_property is not set,
        1 unique solution search is made only after all shift() calls for each
        remaining step from the current step.

        Otherwise, 1 test is made for each remaining step after each shift() call.

        :param max_step: bounded horizon for computations
        :param max_sol: The maximum number of solutions to be returned
        :param vvars: Variables for which solutions must differ.
            In practice, it is a list with the values (Dimacs code)
            of all frontier places of the system.
        :type max_step: <int>
        :type max_sol: <int>
        :type vvars: <list <int>>
        :return: RawSolution objects
            RawSolution objects contain a solution got from SAT solver with all
            variable parameters from the unfolder
        :rtype: <tuple <RawSolution>>
        """
        if LOGGER.getEffectiveLevel() == DEBUG:
            LOGGER.debug("squery_solve :: vvars : %s", vvars)

        # Initialization
        self.init_forward_unfolding()
        # Horizon adjustment
        if self.__list_variant_constraints:
            max_step = min(max_step, len(self.__list_variant_constraints)-1) ## TODO:  -1 ?

        if self.__invariant_property and not self.__final_property:
            # Shift all remaining steps
            while self.__current_step <= max_step:
                self.shift()
            # Solve the problem
            return self.__msolve_constraints(max_sol, vvars)

        else:
            # Check and correct for incoherent data on step number
            # __steps_before_check can't be >= max_step, otherwise
            # __current_step could be > max_step due to shift() of "auto shift loop"
            # and this function will not search any solution,
            # and will return an empty list.
            if self.__steps_before_check >= max_step:
                self.__steps_before_check = max_step - 1

            # Auto shift loop: Shift without checking (optimization)
            # Do not search solutions before the specified limit
            print("squery_solve: begining; current_step:", self.__current_step, "max_step:", max_step)
            while self.__current_step < self.__steps_before_check:
                print("AUTO SHIFT opti")
                self.shift()

            # Search for solutions for each remaining step
            # from __current_step = __steps_before_check
            # (__current_step is incremented by the last shift() above)...
            # ... to max_step excluded.
            # Ex: __steps_before_check = 3, __current_step = 3, max_step = 4
            # => we search solutions only for 1 step (step 4)
            raw_solutions = list()
            while self.__current_step < max_step:
                self.shift()

                temp_raw_solutions = self.__msolve_constraints(max_sol, vvars)
                print("Nb raw_solutions:", len(temp_raw_solutions),
                    "steps_before_check", self.__steps_before_check,
                    "max_step", max_step,
                    "current_step", self.__current_step
                )
                #raw_input("pause")
                # When __steps_before_check is 0 by default, or less than
                # (max_step - 1), we need to search solutions for every steps
                # until max_step is reached.
                # Otherwise, __steps_before_check is set to (maxstep - 1) only
                # to allow us to search solutions for the last step (max_step).

                if temp_raw_solutions:
                    raw_solutions += temp_raw_solutions

            return raw_solutions


###############################################################################
class CLPropertyVisitor(object):
    """
    SigExpression on states and events into a set of clauses
    Type checking must be done.
    """

    def __init__(self, aux_cpt=0):
        self.cpt = aux_cpt         # for auxiliary variable naming
        self.clauses = []          # generated clauses
        self.top = True            # root of the formula?

    def visit_sig_ident(self, tnode):
        """
        ident -> literal
        """
        name = tnode.name
        new_lit = Literal(name, True)
        if self.top:
            self.clauses.append(Clause([new_lit]))
            return None
        return new_lit

    def visit_sig_not(self, node):
        """
        translate a not
        """
        top = self.top
        self.top = False
        # compile operand to nl <=> formula
        newl = node.operand.accept(self)
        notnl = newl.lit_not()
        if top: # we are at the root
            self.clauses.append(Clause([notnl]))
            return None
        return notnl # if we are not at the root

    def visit_sig_sync(self, binnode):
        """
        translate a binary (or/and) expression
        """
        top = self.top
        self.top = False
        # the internal nodes will be affected with the name '_lit'
        name = '_lit'+str(self.cpt)
        self.cpt += 1
        newl = Literal(name, True)
        notnl = Literal(name, False)
        # recursive visits
        operator = binnode.operator
        nl1 = binnode.left_h.accept(self)
        notnl1 = nl1.lit_not()
        nl2 = binnode.right_h.accept(self)
        notnl2 = nl2.lit_not()
        # clauses generation
        if operator == 'and':   # x = lh and rh
            self.clauses.extend([
                Clause([nl1, notnl]),           # not x or not lh
                Clause([nl2, notnl]),           # not x or not rh
                Clause([notnl1, notnl2, newl])  # x or not lh or not rh
            ])

        if operator == 'or':    # x = lh or rh
            self.clauses.extend([
                Clause([notnl1, newl]),         # x or not lh
                Clause([notnl2, newl]),         # x or not rh
                Clause([nl1, nl2, notnl])       # not x or not lh or not rh
            ])

        if top:
            self.clauses.append(Clause([newl]))
            return None
        return newl

    def visit_sig_const(self, exp):
        """
        translate a constant expression
        """
        top = self.top
        if top:
            if exp.is_const_false():
                raise TypeError("No constant False property allowed")
            else: # always present or satisfied
                return None
        # the internal nodes will be affected with the name '_lit'
        name = '_lit'+str(self.cpt)
        self.cpt += 1
        newl = Literal(name, True)

        # clause generation
        if exp.value:
            lit = newl  # x = True
        else:
            lit = newl.lit_not()
        self.clauses.append(Clause([lit]))
        return newl

    # time operators
    def visit_sig_default(self, exp):
        """
        default translation
        """
        top = self.top
        self.top = False
        # the internal nodes will be affected the name '_lit'
        name = '_lit'+str(self.cpt)
        self.cpt += 1
        newl = Literal(name, True)
        notnl = Literal(name, False)
        # recursive visits
        nl1 = exp.left_h.accept(self)
        notnl1 = nl1.lit_not()
        nl2 = exp.right_h.accept(self)
        notnl2 = nl2.lit_not()
        # clause generation: x = lh or rh
        cl1 = Clause([notnl1, newl])        # x or not lh
        cl2 = Clause([notnl2, newl])        # x or not rh
        cl3 = Clause([nl1, nl2, notnl])     # not x or not lh or not rh

        self.clauses.append(cl1)
        self.clauses.append(cl2)
        self.clauses.append(cl3)
        if top:
            self.clauses.append(Clause([newl]))
            return None
        return newl

    def visit_sig_when(self, exp):
        """
        when translation
        """
        top = self.top
        self.top = False
        # the internal nodes will be affected the name '_lit'
        name = '_lit'+str(self.cpt)
        self.cpt += 1
        newl = Literal(name, True)
        notnl = Literal(name, False)
        # recursive visits
        nl1 = exp.left_h.accept(self)
        notnl1 = nl1.lit_not()
        nl2 = exp.right_h.accept(self)
        notnl2 = nl2.lit_not()
        # clause generation: x = lh and rh
        cl1 = Clause([nl1, notnl])           # not x or not lh
        cl2 = Clause([nl2, notnl])           # not x or not rh
        cl3 = Clause([notnl1, notnl2, newl]) # x or not lh or not rh

        self.clauses.append(cl1)
        self.clauses.append(cl2)
        self.clauses.append(cl3)
        if top:
            self.clauses.append(Clause([newl]))
            return None
        return newl