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Entity > Abstract > Class > Relation > Function > BinaryFunction > AssociativeFunction
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AssociativeFunctiondocumentation A BinaryFunction is associative if bracketing has no effect on the value returned by the Function. More precisely, a Function ?FUNCTION is associative just in case (?FUNCTION ?INST1 (?FUNCTION ?INST2 ?INST3)) is equal to (?FUNCTION (?FUNCTION ?INST1 ?INST2) ?INST3), for all ?INST1, ?INST2, and ?INST32001-11-30 13:33:39.0
has axiom
(instance ?FUNCTION AssociativeFunction)
(forall (?INST1 ?INST2 ?INST3)
(instance ?INST1 (DomainFn ?FUNCTION))
(instance ?INST2 (DomainFn ?FUNCTION))
(instance ?INST3 (DomainFn ?FUNCTION)))
(equal (AssignmentFn ?FUNCTION ?INST1 (AssignmentFn ?FUNCTION ?INST1 ?INST2))
(AssignmentFn ?FUNCTION (AssignmentFn ?FUNCTION ?INST1 ?INST2) ?INST3)))))
2001-11-30 13:33:39.0
is a kind of BinaryFunction2001-11-30 13:33:39.0
BinaryFunctionis first domain of distributes2001-11-30 13:33:43.0
is first domain of identityElement2001-11-30 13:33:43.0
is second domain of distributes2001-11-30 13:33:43.0
Classis third domain of domain2001-11-30 13:33:51.0
is third domain of domainSubclass2001-11-30 13:33:51.0
Abstractis disjoint from Physical2001-11-30 13:33:32.0

Kinds of AssociativeFunction :