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Entity > Abstract > Class > Relation > Function > BinaryFunction > CommutativeFunction

CommutativeFunction
subject			fact

CommutativeFunction	documentation A BinaryFunction is commutative if the ordering of the arguments of the function has no effect on the value returned by the function. More precisely, a function ?FUNCTION is commutative just in case (?FUNCTION ?INST1 ?INST2) is equal to (?FUNCTION ?INST2 ?INST1), for all ?INST1 and ?INST2
	has axiom (=> (instance ?FUNCTION CommutativeFunction) (forall (?INST1 ?INST2) (=> (and (instance ?INST1 (DomainFn ?FUNCTION)) (instance ?INST2 (DomainFn ?FUNCTION))) (equal (AssignmentFn ?FUNCTION ?INST1 ?INST2) (AssignmentFn ?FUNCTION ?INST2 ?INST1)))))
	is a kind of BinaryFunction
BinaryFunction	is first domain of distributes
	is first domain of identityElement
	is second domain of distributes
Class	is third domain of domain
	is third domain of domainSubclass
Abstract	is disjoint from Physical

Kinds of CommutativeFunction :

• AdditionFn (9 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (AdditionFn ?NUMBER1 ?NUMBER2) is the arithmetical sum of these numbers
• MaxFn (8 facts) - (MaxFn ?NUMBER1 ?NUMBER2) is the largest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MaxFn returns one of its arguments
• MinFn (8 facts) - (MinFn ?NUMBER1 ?NUMBER2) is the smallest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MinFn returns one of its arguments
• MultiplicationFn (52 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (MultiplicationFn ?NUMBER1 ?NUMBER2) is the arithmetical product of these numbers