Mutual Exclusion by Interpolation

The question of what constraints must hold for a predicate to behave as a (partial) function, is key to understanding the behaviour of a logic program. It has been shown how this question can be answered by combining backward analysis, a form of analysis that propagates determinacy requirements against the control flow, with a component for deriving so-called mutual exclusion conditions. The latter infers conditions sufficient to ensure that if one clause yields an answer then another cannot. This paper addresses the challenge of how to compute these conditions by showing that this problem can be reformulated as that of vertex enumeration. Whilst directly applicable in logic programming, the method might well also find application in reasoning about type classes.