def isThirdNF(relation):
primes = set(attr for key in relation.candidateKeys() for attr in key)
if (not isSecondNF(relation)):
return False
return every(
relation.fdSet, lambda fdItem: set(fdItem[1]).issubset(fdItem[0]) or
relation.validKey(fdItem[0]) or set(fdItem[1]).issubset(primes))
def candidateKeys(self):
keys = []
for i in range(1, len(self.__attributes__) + 1):
# Generate possible combinations and filter out the super sets of existing candidate Keys
possibilities = [
item for item in combinations(self.__attributes__, i)
if not len(keys)
or every(keys, lambda key: not set(key).issubset(item))
]
# add to candidate Keys if it is a valid Key in relation
keys += [item for item in possibilities if self.validKey(item)]
return keys
def candidateKeys(self):
#generating all possible combinations of attributes
keys = []
for i in range(1, len(self.__attributes__) + 1):
possibilities = [
item for item in combinations(self.__attributes__, i)
if not len(keys)
or every(keys, lambda key: not set(key).issubset(item))
]
keys += [item for item in possibilities if self.validKey(item)]
return keys
def cover(fd1, fd2):
return every(
lambda item: fd1.closureSet(item).issubset(fd2.closureSet(item)),
fd1.leftSideSet())
def isBCNF(relation):
if (not isThirdNF(relation)):
return False
return every(relation.fdSet.leftSideSet(),
lambda lhs: relation.validKey(lhs))