planning.py

                new_constraints.add((causal_link[2], action))
                if not self.cyclic(new_constraints):
                    constraints = self.add_const((causal_link[2], action), constraints)
                else:
                    # both promotion and demotion fail
                    print('Unable to resolve a threat caused by', action, 'onto', causal_link)
                    return
        return constraints

    def convert(self, constraints):
        """Convert constraints into a dict of Action to set orderings"""

        graph = dict()
        for constraint in constraints:
            if constraint[0] in graph:
                graph[constraint[0]].add(constraint[1])
            else:
                graph[constraint[0]] = set()
                graph[constraint[0]].add(constraint[1])
        return graph

    def toposort(self, graph):
        """Generate topological ordering of constraints"""

        if len(graph) == 0:
            return

        graph = graph.copy()

        for k, v in graph.items():
            v.discard(k)

        extra_elements_in_dependencies = _reduce(set.union, graph.values()) - set(graph.keys())

        graph.update({element:set() for element in extra_elements_in_dependencies})
        while True:
            ordered = set(element for element, dependency in graph.items() if len(dependency) == 0)
            if not ordered:
                break
            yield ordered
            graph = {element: (dependency - ordered) for element, dependency in graph.items() if element not in ordered}
        if len(graph) != 0:
            raise ValueError('The graph is not acyclic and cannot be linearly ordered')

    def display_plan(self):
        """Display causal links, constraints and the plan"""

        print('Causal Links')
        for causal_link in self.causal_links:
            print(causal_link)

        print('\nConstraints')
        for constraint in self.constraints:
            print(constraint[0], '<', constraint[1])

        print('\nPartial Order Plan')
        print(list(reversed(list(self.toposort(self.convert(self.constraints))))))

    def execute(self, display=True):
        """Execute the algorithm"""

        step = 1
        self.tries = 1
        while len(self.agenda) > 0:
            step += 1
            # select <G, act1> from Agenda
            try:
                G, act1, possible_actions = self.find_open_precondition()
            except IndexError:
                print('Probably Wrong')
                break

            act0 = possible_actions[0]
            # remove <G, act1> from Agenda
            self.agenda.remove((G, act1))

            # For actions with variable number of arguments, use least commitment principle
            # act0_temp, bindings = self.find_action_for_precondition(G)
            # act0 = self.generate_action_object(act0_temp, bindings)

            # Actions = Actions U {act0}
            self.actions.add(act0)

            # Constraints = add_const(start < act0, Constraints)
            self.constraints = self.add_const((self.start, act0), self.constraints)

            # for each CL E CausalLinks do
            #   Constraints = protect(CL, act0, Constraints)
            for causal_link in self.causal_links:
                self.constraints = self.protect(causal_link, act0, self.constraints)

            # Agenda = Agenda U {<P, act0>: P is a precondition of act0}
            for precondition in act0.precond:
                self.agenda.add((precondition, act0))

            # Constraints = add_const(act0 < act1, Constraints)
            self.constraints = self.add_const((act0, act1), self.constraints)

            # CausalLinks U {<act0, G, act1>}
            if (act0, G, act1) not in self.causal_links:
                self.causal_links.append((act0, G, act1))

            # for each A E Actions do
            #   Constraints = protect(<act0, G, act1>, A, Constraints)
            for action in self.actions:
                self.constraints = self.protect((act0, G, act1), action, self.constraints)

            if step > 200:
                print('Couldn\'t find a solution')
                return None, None

        if display:
            self.display_plan()
        else:
            return self.constraints, self.causal_links                


def spare_tire_graphplan():
    """Solves the spare tire problem using GraphPlan"""
    return GraphPlan(spare_tire()).execute()

def three_block_tower_graphplan():
    """Solves the Sussman Anomaly problem using GraphPlan"""
    return GraphPlan(three_block_tower()).execute()

def air_cargo_graphplan():
    """Solves the air cargo problem using GraphPlan"""
    return GraphPlan(air_cargo()).execute()

def have_cake_and_eat_cake_too_graphplan():
    """Solves the cake problem using GraphPlan"""
    return [GraphPlan(have_cake_and_eat_cake_too()).execute()[1]]

def shopping_graphplan():
    """Solves the shopping problem using GraphPlan"""
    return GraphPlan(shopping_problem()).execute()

def socks_and_shoes_graphplan():
    """Solves the socks and shoes problem using GraphpPlan"""
    return GraphPlan(socks_and_shoes()).execute()

def simple_blocks_world_graphplan():
    """Solves the simple blocks world problem"""
    return GraphPlan(simple_blocks_world()).execute()


class HLA(Action):
    """
    Define Actions for the real-world (that may be refined further), and satisfy resource
    constraints.
    """
    unique_group = 1

    def __init__(self, action, precond=None, effect=None, duration=0,
                 consume=None, use=None):
        """
        As opposed to actions, to define HLA, we have added constraints.
        duration holds the amount of time required to execute the task
        consumes holds a dictionary representing the resources the task consumes
        uses holds a dictionary representing the resources the task uses
        """
        precond = precond or [None]
        effect = effect or [None]
        super().__init__(action, precond, effect)
        self.duration = duration
        self.consumes = consume or {}
        self.uses = use or {}
        self.completed = False
        # self.priority = -1 #  must be assigned in relation to other HLAs
        # self.job_group = -1 #  must be assigned in relation to other HLAs

    def do_action(self, job_order, available_resources, kb, args):
        """
        An HLA based version of act - along with knowledge base updation, it handles
        resource checks, and ensures the actions are executed in the correct order.
        """
        # print(self.name)
        if not self.has_usable_resource(available_resources):
            raise Exception('Not enough usable resources to execute {}'.format(self.name))
        if not self.has_consumable_resource(available_resources):
            raise Exception('Not enough consumable resources to execute {}'.format(self.name))
        if not self.inorder(job_order):
            raise Exception("Can't execute {} - execute prerequisite actions first".
                            format(self.name))
        kb = super().act(kb, args)  # update knowledge base
        for resource in self.consumes:  # remove consumed resources
            available_resources[resource] -= self.consumes[resource]
        self.completed = True  # set the task status to complete
        return kb

    def has_consumable_resource(self, available_resources):
        """
        Ensure there are enough consumable resources for this action to execute.
        """
        for resource in self.consumes:
            if available_resources.get(resource) is None:
                return False
            if available_resources[resource] < self.consumes[resource]:
                return False
        return True

    def has_usable_resource(self, available_resources):
        """
        Ensure there are enough usable resources for this action to execute.
        """
        for resource in self.uses:
            if available_resources.get(resource) is None:
                return False
            if available_resources[resource] < self.uses[resource]:
                return False
        return True

    def inorder(self, job_order):
        """
        Ensure that all the jobs that had to be executed before the current one have been
        successfully executed.
        """
        for jobs in job_order:
            if self in jobs:
                for job in jobs:
                    if job is self:
                        return True
                    if not job.completed:
                        return False
        return True


class Problem(PlanningProblem):
    """
    Define real-world problems by aggregating resources as numerical quantities instead of
    named entities.

    This class is identical to PDLL, except that it overloads the act function to handle
    resource and ordering conditions imposed by HLA as opposed to Action.
    """
    def __init__(self, init, goals, actions, jobs=None, resources=None):
        super().__init__(init, goals, actions)
        self.jobs = jobs
        self.resources = resources or {}

    def act(self, action):
        """
        Performs the HLA given as argument.

        Note that this is different from the superclass action - where the parameter was an
        Expression. For real world problems, an Expr object isn't enough to capture all the
        detail required for executing the action - resources, preconditions, etc need to be
        checked for too.
        """
        args = action.args
        list_action = first(a for a in self.actions if a.name == action.name)
        if list_action is None:
            raise Exception("Action '{}' not found".format(action.name))
        self.init = list_action.do_action(self.jobs, self.resources, self.init, args).clauses

    def refinements(hla, state, library):  # refinements may be (multiple) HLA themselves ...
        """
        state is a Problem, containing the current state kb
        library is a dictionary containing details for every possible refinement. eg:
        {
        'HLA': [
            'Go(Home, SFO)',
            'Go(Home, SFO)',
            'Drive(Home, SFOLongTermParking)',
            'Shuttle(SFOLongTermParking, SFO)',
            'Taxi(Home, SFO)'
            ],
        'steps': [
            ['Drive(Home, SFOLongTermParking)', 'Shuttle(SFOLongTermParking, SFO)'],
            ['Taxi(Home, SFO)'],
            [],
            [],
            []
            ],
        # empty refinements indicate a primitive action
        'precond': [
            ['At(Home) & Have(Car)'],
            ['At(Home)'],
            ['At(Home) & Have(Car)'],
            ['At(SFOLongTermParking)'],
            ['At(Home)']
            ],
        'effect': [
            ['At(SFO) & ~At(Home)'],
            ['At(SFO) & ~At(Home)'],
            ['At(SFOLongTermParking) & ~At(Home)'],
            ['At(SFO) & ~At(SFOLongTermParking)'],
            ['At(SFO) & ~At(Home)']
            ]
        }
        """
        e = Expr(hla.name, hla.args)
        indices = [i for i, x in enumerate(library['HLA']) if expr(x).op == hla.name]
        for i in indices:
            actions = []
            for j in range(len(library['steps'][i])):
                # find the index of the step [j]  of the HLA 
                index_step = [k for k,x in enumerate(library['HLA']) if x == library['steps'][i][j]][0]
                precond = library['precond'][index_step][0] # preconditions of step [j]
                effect = library['effect'][index_step][0] # effect of step [j]
                actions.append(HLA(library['steps'][i][j], precond, effect))
            yield actions

    def hierarchical_search(problem, hierarchy):
        """
        [Figure 11.5] 'Hierarchical Search, a Breadth First Search implementation of Hierarchical
        Forward Planning Search'
        The problem is a real-world problem defined by the problem class, and the hierarchy is
        a dictionary of HLA - refinements (see refinements generator for details)
        """
        act = Node(problem.actions[0])
        frontier = deque()
        frontier.append(act)
        while True:
            if not frontier:
                return None
            plan = frontier.popleft()
            print(plan.state.name)
            hla = plan.state  # first_or_null(plan)
            prefix = None
            if plan.parent:
                prefix = plan.parent.state.action  # prefix, suffix = subseq(plan.state, hla)
            outcome = Problem.result(problem, prefix)
            if hla is None:
                if outcome.goal_test():
                    return plan.path()
            else:
                print("else")
                for sequence in Problem.refinements(hla, outcome, hierarchy):
                    print("...")
                    frontier.append(Node(plan.state, plan.parent, sequence))

    def result(state, actions):
        """The outcome of applying an action to the current problem"""
        for a in actions: 
            if a.check_precond(state, a.args):
                state = a(state, a.args).clauses
        return state
    

    def angelic_search(problem, hierarchy, initialPlan):
        """
	[Figure 11.8] A hierarchical planning algorithm that uses angelic semantics to identify and
	commit to high-level plans that work while avoiding high-level plans that don’t. 
	The predicate MAKING-PROGRESS checks to make sure that we aren’t stuck in an infinite regression
	of refinements. 
	At top level, call ANGELIC -SEARCH with [Act ] as the initialPlan .

        initialPlan contains a sequence of HLA's with angelic semantics 

        The possible effects of an angelic HLA in initialPlan are : 
        ~ : effect remove
        $+: effect possibly add
        $-: effect possibly remove
        $$: possibly add or remove
	"""
        frontier = deque(initialPlan)
        while True: 
            if not frontier:
                return None
            plan = frontier.popleft() # sequence of HLA/Angelic HLA's 
            opt_reachable_set = Problem.reach_opt(problem.init, plan)
            pes_reachable_set = Problem.reach_pes(problem.init, plan)
            if problem.intersects_goal(opt_reachable_set): 
                if Problem.is_primitive( plan, hierarchy ): 
                    return ([x for x in plan.action])
                guaranteed = problem.intersects_goal(pes_reachable_set) 
                if guaranteed and Problem.making_progress(plan, plan):
                    final_state = guaranteed[0] # any element of guaranteed 
                    #print('decompose')
                    return Problem.decompose(hierarchy, problem, plan, final_state, pes_reachable_set)
                (hla, index) = Problem.find_hla(plan, hierarchy) # there should be at least one HLA/Angelic_HLA, otherwise plan would be primitive.
                prefix = plan.action[:index-1]
                suffix = plan.action[index+1:]
                outcome = Problem(Problem.result(problem.init, prefix), problem.goals , problem.actions )
                for sequence in Problem.refinements(hla, outcome, hierarchy): # find refinements
                    frontier.append(Angelic_Node(outcome.init, plan, prefix + sequence+ suffix, prefix+sequence+suffix))


    def intersects_goal(problem, reachable_set):
        """
        Find the intersection of the reachable states and the goal
        """
        return [y for x in list(reachable_set.keys()) for y in reachable_set[x] if all(goal in y for goal in problem.goals)] 


    def is_primitive(plan,  library):
        """
        checks if the hla is primitive action 
        """
        for hla in plan.action: 
            indices = [i for i, x in enumerate(library['HLA']) if expr(x).op == hla.name]
            for i in indices:
                if library["steps"][i]: 
                    return False
        return True
             


    def reach_opt(init, plan): 
        """
        Finds the optimistic reachable set of the sequence of actions in plan 
        """
        reachable_set = {0: [init]}
        optimistic_description = plan.action #list of angelic actions with optimistic description
        return Problem.find_reachable_set(reachable_set, optimistic_description)
 

    def reach_pes(init, plan): 
        """ 
        Finds the pessimistic reachable set of the sequence of actions in plan
        """
        reachable_set = {0: [init]}
        pessimistic_description = plan.action_pes # list of angelic actions with pessimistic description
        return Problem.find_reachable_set(reachable_set, pessimistic_description)

    def find_reachable_set(reachable_set, action_description):
        """
	Finds the reachable states of the action_description when applied in each state of reachable set.
	"""
        for i in range(len(action_description)):
            reachable_set[i+1]=[]
            if type(action_description[i]) is Angelic_HLA:
                possible_actions = action_description[i].angelic_action()
            else: 
                possible_actions = action_description
            for action in possible_actions:
                for state in reachable_set[i]:
                    if action.check_precond(state , action.args) :
                        if action.effect[0] :
                            new_state = action(state, action.args).clauses
                            reachable_set[i+1].append(new_state)
                        else: 
                            reachable_set[i+1].append(state)
        return reachable_set

    def find_hla(plan, hierarchy):
        """
        Finds the the first HLA action in plan.action, which is not primitive
        and its corresponding index in plan.action
        """
        hla = None
        index = len(plan.action)
        for i in range(len(plan.action)): # find the first HLA in plan, that is not primitive
            if not Problem.is_primitive(Node(plan.state, plan.parent, [plan.action[i]]), hierarchy):
                hla = plan.action[i] 
                index = i
                break
        return (hla, index)
	
    def making_progress(plan, initialPlan):
        """ 
        Not correct

        Normally should from infinite regression of refinements 
        
        Only case covered: when plan contains one action (then there is no regression to be done)  
        """
        if (len(plan.action)==1):
            return False
        return True 

    def decompose(hierarchy, s_0, plan, s_f, reachable_set):
        solution = [] 
        while plan.action_pes: 
            action = plan.action_pes.pop()
            i = max(reachable_set.keys())
            if (i==0): 
                return solution
            s_i = Problem.find_previous_state(s_f, reachable_set,i, action) 
            problem = Problem(s_i, s_f , plan.action)
            j=0
            for x in Problem.angelic_search(problem, hierarchy, [Angelic_Node(s_i, Node(None), [action],[action])]):
                solution.insert(j,x)
                j+=1
            s_f = s_i
        return solution


    def find_previous_state(s_f, reachable_set, i, action):
        """
        Given a final state s_f and an action finds a state s_i in reachable_set 
        such that when action is applied to state s_i returns s_f.  
        """
        s_i = reachable_set[i-1][0]
        for state in reachable_set[i-1]:
            if s_f in [x for x in Problem.reach_pes(state, Angelic_Node(state, None, [action],[action]))[1]]:
                s_i =state
                break
        return s_i


def job_shop_problem():
    """
    [Figure 11.1] JOB-SHOP-PROBLEM

    A job-shop scheduling problem for assembling two cars,
    with resource and ordering constraints.

    Example:
    >>> from planning import *
    >>> p = job_shop_problem()
    >>> p.goal_test()
    False
    >>> p.act(p.jobs[1][0])
    >>> p.act(p.jobs[1][1])
    >>> p.act(p.jobs[1][2])
    >>> p.act(p.jobs[0][0])
    >>> p.act(p.jobs[0][1])
    >>> p.goal_test()
    False
    >>> p.act(p.jobs[0][2])
    >>> p.goal_test()
    True
    >>>
    """
    resources = {'EngineHoists': 1, 'WheelStations': 2, 'Inspectors': 2, 'LugNuts': 500}

    add_engine1 = HLA('AddEngine1', precond='~Has(C1, E1)', effect='Has(C1, E1)', duration=30, use={'EngineHoists': 1})
    add_engine2 = HLA('AddEngine2', precond='~Has(C2, E2)', effect='Has(C2, E2)', duration=60, use={'EngineHoists': 1})
    add_wheels1 = HLA('AddWheels1', precond='~Has(C1, W1)', effect='Has(C1, W1)', duration=30, use={'WheelStations': 1}, consume={'LugNuts': 20})
    add_wheels2 = HLA('AddWheels2', precond='~Has(C2, W2)', effect='Has(C2, W2)', duration=15, use={'WheelStations': 1}, consume={'LugNuts': 20})
    inspect1 = HLA('Inspect1', precond='~Inspected(C1)', effect='Inspected(C1)', duration=10, use={'Inspectors': 1})
    inspect2 = HLA('Inspect2', precond='~Inspected(C2)', effect='Inspected(C2)', duration=10, use={'Inspectors': 1})

    actions = [add_engine1, add_engine2, add_wheels1, add_wheels2, inspect1, inspect2]

    job_group1 = [add_engine1, add_wheels1, inspect1]
    job_group2 = [add_engine2, add_wheels2, inspect2]

    return Problem(init='Car(C1) & Car(C2) & Wheels(W1) & Wheels(W2) & Engine(E2) & Engine(E2) & ~Has(C1, E1) & ~Has(C2, E2) & ~Has(C1, W1) & ~Has(C2, W2) & ~Inspected(C1) & ~Inspected(C2)',
                   goals='Has(C1, W1) & Has(C1, E1) & Inspected(C1) & Has(C2, W2) & Has(C2, E2) & Inspected(C2)',
                   actions=actions,
                   jobs=[job_group1, job_group2],
                   resources=resources)


def go_to_sfo():
    """Go to SFO Problem"""

    go_home_sfo1 = HLA('Go(Home, SFO)', precond='At(Home) & Have(Car)', effect='At(SFO) & ~At(Home)')
    go_home_sfo2 = HLA('Go(Home, SFO)', precond='At(Home)', effect='At(SFO) & ~At(Home)')
    drive_home_sfoltp = HLA('Drive(Home, SFOLongTermParking)', precond='At(Home) & Have(Car)', effect='At(SFOLongTermParking) & ~At(Home)')
    shuttle_sfoltp_sfo = HLA('Shuttle(SFOLongTermParking, SFO)', precond='At(SFOLongTermParking)', effect='At(SFO) & ~At(SFOLongTermParking)')
    taxi_home_sfo = HLA('Taxi(Home, SFO)', precond='At(Home)', effect='At(SFO) & ~At(Home)')

    actions = [go_home_sfo1, go_home_sfo2, drive_home_sfoltp, shuttle_sfoltp_sfo, taxi_home_sfo]

    library = {
        'HLA': [
            'Go(Home, SFO)',
            'Go(Home, SFO)',
            'Drive(Home, SFOLongTermParking)',
            'Shuttle(SFOLongTermParking, SFO)',
            'Taxi(Home, SFO)'
        ],
        'steps': [
            ['Drive(Home, SFOLongTermParking)', 'Shuttle(SFOLongTermParking, SFO)'],
            ['Taxi(Home, SFO)'],
            [],
            [],
            []
        ],
        'precond': [
            ['At(Home) & Have(Car)'],
            ['At(Home)'],
            ['At(Home) & Have(Car)'],
            ['At(SFOLongTermParking)'],
            ['At(Home)']
        ],
        'effect': [
            ['At(SFO) & ~At(Home)'],
            ['At(SFO) & ~At(Home)'],
            ['At(SFOLongTermParking) & ~At(Home)'],
            ['At(SFO) & ~At(SFOLongTermParking)'],
            ['At(SFO) & ~At(Home)']
        ]
    }

    return Problem(init='At(Home)', goals='At(SFO)', actions=actions), library


class Angelic_HLA(HLA):
    """
    Define Actions for the real-world (that may be refined further), under angelic semantics
    """
    
    def __init__(self, action, precond , effect, duration =0, consume = None, use = None):
        super().__init__(action, precond, effect, duration, consume, use)


    def convert(self, clauses):
        """
        Converts strings into Exprs
        An HLA with angelic semantics can achieve the effects of simple HLA's (add / remove a variable ) 
        and furthermore can have following effects on the variables: 
            Possibly add variable    ( $+ )
            Possibly remove variable ( $- )
            Possibly add or remove a variable ( $$ )

        Overrides HLA.convert function
        """ 
        lib = {'~': 'Not', 
                '$+': 'PosYes',
               '$-': 'PosNot',
               '$$' : 'PosYesNot'}

        if isinstance(clauses, Expr):
            clauses = conjuncts(clauses)
            for i in range(len(clauses)):
                for ch in lib.keys():
                    if clauses[i].op == ch:
                        clauses[i] = expr( lib[ch] + str(clauses[i].args[0]))

        elif isinstance(clauses, str):
            for ch in lib.keys():
                clauses = clauses.replace(ch, lib[ch])
            if len(clauses) > 0:
                clauses = expr(clauses)

            try:
                clauses = conjuncts(clauses)
            except AttributeError:
                pass

        return clauses

        
        

    def angelic_action(self):
        """
        Converts a high level action (HLA) with angelic semantics into all of its corresponding high level actions (HLA). 
        An HLA with angelic semantics can achieve the effects of simple HLA's (add / remove a variable) 
        and furthermore can have following effects for each variable: 

            Possibly add variable ( $+: 'PosYes' )        --> corresponds to two HLAs: 
                                                                HLA_1: add variable  
                                                                HLA_2: leave variable unchanged

            Possibly remove variable ( $-: 'PosNot' )     --> corresponds to two HLAs:
                                                                HLA_1: remove variable
                                                                HLA_2: leave variable unchanged

            Possibly add / remove a variable ( $$: 'PosYesNot' )  --> corresponds to three HLAs: 
                                                                        HLA_1: add variable
                                                                        HLA_2: remove variable
                                                                        HLA_3: leave variable unchanged 


            example: the angelic action with effects possibly add A and possibly add or remove B corresponds to the following 6 effects of HLAs:
            
            
            '$+A & $$B':    HLA_1: 'A & B'   (add A and add B)
                            HLA_2: 'A & ~B'  (add A and remove B)
                            HLA_3: 'A'       (add A)
                            HLA_4: 'B'       (add B)
                            HLA_5: '~B'      (remove B)
                            HLA_6: ' '       (no effect)  

        """

        effects=[[]]
        for clause in self.effect:
            (n,w) = Angelic_HLA.compute_parameters(clause, effects)
            effects = effects*n # create n copies of effects 
            it=range(1)
            if len(effects)!=0:
                # split effects into n sublists (seperate n copies created in compute_parameters)
                it = range(len(effects)//n)
            for i in it:
                if effects[i]:
                    if clause.args: 
                        effects[i] = expr(str(effects[i]) + '&' + str(Expr(clause.op[w:],clause.args[0]))) # make changes in the ith part of effects
                        if n==3:
                            effects[i+len(effects)//3]= expr(str(effects[i+len(effects)//3]) + '&' + str(Expr(clause.op[6:],clause.args[0])))
                    else: 
                        effects[i] = expr(str(effects[i]) + '&' + str(expr(clause.op[w:]))) # make changes in the ith part of effects
                        if n==3: 
                            effects[i+len(effects)//3] = expr(str(effects[i+len(effects)//3]) + '&' + str(expr(clause.op[6:])))

                else: 
                    if clause.args: 
                        effects[i] = Expr(clause.op[w:], clause.args[0]) # make changes in the ith part of effects
                        if n==3: 
                            effects[i+len(effects)//3] = Expr(clause.op[6:], clause.args[0])

                    else: 
                        effects[i] = expr(clause.op[w:])  # make changes in the ith part of effects
                        if n==3: 
                            effects[i+len(effects)//3] = expr(clause.op[6:])
            #print('effects',  effects)

        return [ HLA(Expr(self.name, self.args), self.precond, effects[i] ) for i in range(len(effects)) ]


    def compute_parameters(clause, effects):
        """ 
        computes n,w 
        
        n = number of HLA effects that the anelic HLA corresponds to
        w = length of representation of angelic HLA effect 

                    n = 1, if effect is add
                    n = 1, if effect is remove
                    n = 2, if effect is possibly add
                    n = 2, if effect is possibly remove
                    n = 3, if effect is possibly add or remove

        """
        if clause.op[:9] == 'PosYesNot':
            # possibly add/remove variable: three possible effects for the variable 
            n=3
            w=9
        elif clause.op[:6] == 'PosYes': # possibly add variable: two possible effects for the variable
            n=2
            w=6
        elif clause.op[:6] == 'PosNot': # possibly remove variable: two possible effects for the variable
            n=2
            w=3 # We want to keep 'Not' from 'PosNot' when adding action
        else:   # variable or ~variable 
            n=1
            w=0
        return (n,w)


class Angelic_Node(Node):
    """ 
    Extends the class Node. 
    self.action:     contains the optimistic description of an angelic HLA
    self.action_pes: contains the pessimistic description of an angelic HLA
    """

    def __init__(self, state, parent=None, action_opt=None, action_pes=None,  path_cost=0):
        super().__init__(state, parent, action_opt , path_cost)
        self.action_pes = action_pes