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AssociativeFunction(associative function)
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| appearance as argument number 1 |
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| (subclass AssociativeFunction BinaryFunction) | Merge.kif 3522-3522 | Associative function is a subclass of binary function |
| (documentation AssociativeFunction EnglishLanguage "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 ?INST3.") | Merge.kif 3524-3529 | Associative function is a subclass of binary function |
| (externalImage AssociativeFunction "http://upload.wikimedia.org/wikipedia/ commons/ e/ eb/ RelativeComplement.png") | pictureList.kif 8351-8351 | Associative function is a subclass of binary function |
| appearance as argument number 2 |
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| antecedent |
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| (=> (instance ?FUNCTION AssociativeFunction) (forall (?INST1 ?INST2 ?INST3 ?CLASS) (=> (and (domain ?FUNCTION 1 ?CLASS) (instance ?INST1 ?CLASS) (instance ?INST2 ?CLASS) (instance ?INST3 ?CLASS)) (equal (AssignmentFn ?FUNCTION ?INST1 (AssignmentFn ?FUNCTION ?INST2 ?INST3)) (AssignmentFn ?FUNCTION (AssignmentFn ?FUNCTION ?INST1 ?INST2) ?INST3))))) |
Merge.kif 3531-3541 | If X is an instance of associative function, then For all Entities Y, Z, and W and Class V: if the number 1 argument of X is an instance of V, Y is an instance of V, Z is an instance of V, and W is an instance of V, then equal X(Y and X(Z and W)) and X(X(Y and Z) and W) |
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