def getClosure(formula, closure):
"""
Function that generates the closure of a temporal formula.
:param formula: Temporal formula that we want to find the closure
:param closure: Empty list to store the subformulas of the closure
:type formula: Formula
:type closure: List
:Example:
>>> from closure import *
>>> phi = Formula({"<>": {"^":{"":"in=true","~":{"o":"x=2"}}}})
>>> closure = []
>>> getClosure(phi,closure)
>>> for formula in closure:
... print formula.getFormula()
...
{'<>': {'^': {'': 'in=true', '~': {'o': 'x=2'}}}}
{'~': {'<>': {'^': {'': 'in=true', '~': {'o': 'x=2'}}}}}
{'o': {'<>': {'^': {'': 'in=true', '~': {'o': 'x=2'}}}}}
{'~': {'o': {'<>': {'^': {'': 'in=true', '~': {'o': 'x=2'}}}}}}
{'o': {'~': {'<>': {'^': {'': 'in=true', '~': {'o': 'x=2'}}}}}}
{'^': {'': 'in=true', '~': {'o': 'x=2'}}}
{'~': {'^': {'': 'in=true', '~': {'o': 'x=2'}}}}
{'': 'in=true'}
{'~': 'in=true'}
{'o': 'x=2'}
{'~': {'o': 'x=2'}}
{'o': {'~': 'x=2'}}
{'': 'x=2'}
{'~': 'x=2'}
.. note::
This function is based on the conditions shown in the section 6.1 of the thesis document.
"""
if formula.isNegativeFormula():
formula = Formula(formula.getValues())
subformula = formula.getValues()
if formula.isProposition(): # PROPOSITION rule
closure.append(Formula({"": subformula})) # p
closure.append(Formula({"~": subformula})) # ~p
elif formula.getConnective() == "^" : # AND rule
subformulas = formula.getSubFormulas()
closure.append(Formula({"^": subformula})) # phi ^ psi
closure.append(Formula({"~": {"^": subformula}})) # ~ (phi ^ psi)
getClosure(subformulas[0],closure)
getClosure(subformulas[1],closure)
elif formula.getConnective() == "v" : # OR rule
subformulas = formula.getSubFormulas()
closure.append(Formula({"v": subformula})) # phi v psi
closure.append(Formula({"~": {"v": subformula}})) # ~ (phi v psi)
getClosure(subformulas[0],closure)
getClosure(subformulas[1],closure)
elif formula.getConnective() == "o" : # NEXT rule
closure.append(Formula({"o": subformula})) # o phi
closure.append(Formula({"~": {"o": subformula}})) # ~o phi
closure.append(Formula({"o": {"~": subformula}})) # o~ phi
getClosure(Formula(formula.getValues()),closure)
elif formula.getConnective() == "<>": # FUTURE rule
closure.append(Formula({"<>": subformula})) # <> phi
closure.append(Formula({"~": {"<>": subformula}})) # ~<> phi
closure.append(Formula({"o": {"<>": subformula}})) # o<> phi
closure.append(Formula({"~": {"o": {"<>": subformula}}})) # ~o<> phi
closure.append(Formula({"o": {"~": {"<>": subformula}}})) # o~<> phi
getClosure(Formula(formula.getValues()),closure)
elif formula.getConnective() == "[]": # GLOBALLY rule
closure.append(Formula({"[]": subformula})) # [] phi
closure.append(Formula({"~": {"[]": subformula}})) # ~[] phi
closure.append(Formula({"o": {"[]": subformula}})) # o[] phi
closure.append(Formula({"~": {"o": {"[]": subformula}}})) # ~o[] phi
closure.append(Formula({"o": {"~": {"[]": subformula}}})) # o~[] phi
getClosure(Formula(formula.getValues()),closure)
