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engine.py
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engine.py
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class CNF:
def __init__(self, propositional):
self.propositional = propositional
print("Constructor is called for '{}'".format(propositional))
def __str__(self):
print("String is called!")
def __contains__(self):
print("Contains is called!")
# Reduces the operators, if "and" is present inside "and" or "or" inside "or"
# Example : ["and", "A", ["and", "B", "C"]] should be ["and", "A", "B", "C"]
def reduceOperators(self, formula):
print("reduceOperators is running...")
if (isinstance(formula, str)):
print("isinstance is called!")
return formula
operator = formula[0]
literals = []
propositions = []
for index, item in enumerate(formula):
if (index > 0):
print("condition 03: index > 0")
if (isinstance(item, str)):
print("condition 04")
literals.append(item)
elif (isinstance(item, list)):
print("condition 05")
propositions.append(self.reduceOperators(item))
newFormula = literals
for item in propositions:
if (isinstance(item, list) and item[0] == operator):
print("condition 06")
for i, clause in enumerate(item):
if (i > 0):
print("condition 07")
newFormula.append(clause)
else:
print("condition 08")
newFormula.append(item)
newFormula.insert(0, operator)
return newFormula
def vlrTOlvr(self, formula):
if(len(formula)==3):
if(len(formula[1]) == 3):
self.vlrTOlvr(formula[1])
print("({}){}({})".format(formula[1], formula[0], formula[2]))
if (len(formula[2]) == 3):
self.vlrTOlvr(formula[2])
print("({}){}({})".format(formula[1], formula[0], formula[2]))
# Removes duplicate elements from "and" and "or"
# Example : ["and", "A", "A"] should be "A"
def removeDuplicates(self, formula):
if (isinstance(formula, str) or (
isinstance(formula, list) and formula[0] == "not" and isinstance(formula[1], str))):
return formula
for i, checkItem in enumerate(formula):
if (i > 0):
for j, item in reversed(list(enumerate(formula))):
if (j > i):
if (isinstance(item, list)):
newItem = self.removeDuplicates(item)
formula.insert(j, newItem)
formula.remove(item)
if (checkItem == item):
formula.remove(item)
if (isinstance(formula, list) and formula[0] != "not" and len(formula) < 3):
return formula[1]
return formula
# Sorts the literals and lists in the formula (will be used for removing duplicate items in list)
# The literals are in the beginning followed by lists. And the "and" list is present in the end
def sort(self, formula):
if (isinstance(formula, str)):
return formula
operator = formula[0]
if (operator == "->"):
return formula
literals = []
propositions = []
for index, item in enumerate(formula):
if (index > 0):
if (isinstance(item, str)):
literals.append(item)
elif (isinstance(item, list)):
propositions.append(self.sort(item))
if (len(literals) > 0):
literals.sort()
if (len(propositions) > 0):
propositions = sorted(propositions, key=lambda proposition: proposition[0], reverse=True)
newFormula = literals + propositions
newFormula.insert(0, operator)
return newFormula
# Converts to CNF by taking different cases separately
def convert(self, formula):
if (isinstance(formula, str)):
return formula
elif (isinstance(formula, list)):
# A => B ---> ~A | B
if (formula[0] == "->"):
return self.convert(["or", self.convert(["not", self.convert(formula[1])]), self.convert(formula[2])])
# A <=> B ---> (~A | B) & (A | ~B)
elif (formula[0] == "iff"):
return self.convert("and", self.convert(["or", self.convert(["not", formula[1]]), formula[2]]), self.convert(["or", formula[1], self.convert(["not", self.formula[2]])]))
elif (formula[0] == "not"):
# ~p
if (isinstance(formula[1], str)):
return formula
# ~~p ---> p
elif (isinstance(formula[1], list) and (formula[1])[0] == "not"):
return self.convert((formula[1])[1])
# ~(A & B & C & ...) ---> ~A | ~B | ~C | ....
elif (isinstance(formula[1], list) and (formula[1])[0] == "and"):
disjuncts = []
for index, item in enumerate(formula[1]):
if (index > 0):
disjuncts.append(self.convert(["not", item]))
disjuncts.insert(0, "or")
return self.convert(disjuncts)
# ~(A | B | C | ...) ---> ~A & ~B & ~C & ....
elif (isinstance(formula[1], list) and (formula[1])[0] == "or"):
conjuncts = []
for index, item in enumerate(formula[1]):
if (index > 0):
conjuncts.append(self.convert(["not", item]))
conjuncts.insert(0, "and")
return self.convert(conjuncts)
# ~(A => B) ---> A & ~B
elif (isinstance(formula[1], list) and ((formula[1])[0] == "->")):
return self.convert(["and", self.convert((formula[1])[1]), ["not", self.convert((formula[1][2]))]])
elif (isinstance(formula[1], list) and (formula[1])[0] == "iff"):
return self.convert(["not", self.convert(formula[1])])
elif (formula[0] == "or"):
# A | A ---> A
formula = self.sort(formula)
formula = self.removeDuplicates(formula)
# Handling the case ["or", "A", ["or", "B", "C"]]
formula = self.reduceOperators(formula)
# The order will be messed up when the redundant operators are removed
# Handling the case when the formula is reduced.
# For instance A or A is reduced to A
formula = self.sort(formula)
if (len(formula) == 1):
return formula
if ((isinstance(formula[-1], list) and (formula[-1])[0] == "and")):
# A | (B & C & D & ...) ---> (A | B) & (A | C) & (A | D) & ...
conjuncts = []
for i, item in enumerate(formula[-1]):
if (i > 0):
conjuncts.append(["or", formula[-2], item])
conjuncts.insert(0, "and")
# If only 2 items, then remove them and also remove OR
if (len(formula) < 4):
return self.convert(conjuncts)
else:
formula.remove(formula[-1])
formula.remove(formula[-1])
formula.append(conjuncts)
return self.convert(formula)
# Case A OR B,
elif ((isinstance(formula[1], str) and isinstance(formula[2], str)) or (
isinstance(formula[1], str) and isinstance(formula[2], list) and (formula[2])[
0] == "not" and isinstance((formula[2])[1], str)) or (
isinstance(formula[2], str) and isinstance(formula[1], list) and (formula[1])[
0] == "not" and isinstance((formula[1])[1], str))):
formula.append(["or", formula[1], formula[2]])
formula.remove(formula[1])
formula.remove(formula[1])
formula = self.reduceOperators(formula)
formula = self.sort(formula)
return formula
# Case !A OR !B
elif (isinstance(formula[1], list) and (formula[1])[0] == "not" and isinstance((formula[1])[1], str) and isinstance(formula[2], list) and (formula[2])[0] == "not" and isinstance((formula[2])[1], str)):
return formula
# For any other operator compute the inner operator after or
else:
disjuncts = []
for i, item in enumerate(formula):
if (i > 0):
disjuncts.append(self.convert(item))
disjuncts.insert(0, "or")
return self.convert(disjuncts)
elif (formula[0] == "and"):
# Handling the case ["and", "A", ["or", "C", "D"], ["or", "D", "C"]]
formula = self.sort(formula)
formula = self.removeDuplicates(formula)
# Handling the case ["and", "A", ["and", "B", "C"]]
formula = self.reduceOperators(formula)
# The order will be messed up when the redundant operators are removed
formula = self.sort(formula)
if (len(formula) == 1):
return formula
disjuncts = []
for i, item in enumerate(formula):
if (i > 0):
disjuncts.append(self.convert(item))
disjuncts.insert(0, "and")
disjuncts = self.reduceOperators(disjuncts)
return disjuncts