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Entity > Abstract > Class > Relation > Function > BinaryFunction > AssociativeFunction |

AssociativeFunction | ||||

subject | fact |

AssociativeFunction | 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 documentationequal to (?FUNCTION (?FUNCTION ?INST1 ?INST2) ?INST3), for all ?INST1, ?INST2, and ?INST3 | |

has axiom (=> | ||

is a kind of BinaryFunction | ||

BinaryFunction | is first domain ofdistributes | |

is first domain ofidentityElement | ||

is second domain ofdistributes | ||

Class | is third domain ofdomain | |

is third domain ofdomainSubclass | ||

Abstract | is Physicaldisjoint from |

**Kinds of AssociativeFunction** :

*AdditionFn*(9 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (AdditionFn ?NUMBER1 ?NUMBER2) is the arithmetical sum of these numbers*DivisionFn*(15 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (DivisionFn ?NUMBER1 ?NUMBER2) is the result of dividing ?NUMBER1 by ?NUMBER2. An exception occurs when ?NUMBER1 = 1, in which case (DivisionFn ?NUMBER1 ?NUMBER2) is the reciprocal of ?NUMBER2*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*SubtractionFn*(10 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (SubtractionFn ?NUMBER1 ?NUMBER2) is the arithmetical difference between ?NUMBER1 and ?NUMBER2, i.e. ?NUMBER1 minus ?NUMBER2. An exception occurs when ?NUMBER1 is equal to 0, in which case (SubtractionFn ?NUMBER1 ?NUMBER2) is the negation of ?NUMBER2