## Comparing Function Tables Using Partition Predicates

Dr. Zbig Dudek

Software Engineering Research Group

CRL, McMaster University,

Hamilton, Ontario, Canada L8S 4K1

### Abstract

Function and relation tables [P2] have proven to be useful for the formal documentation of software
systems. In this paper we consider the problem of semantic equivalence of two function tables and reduce
it to the two seemingly simpler problems: the first one is generating refined partitions of the domains of
the functions considered; and the second is determining whether two functional expressions associated
with the refined partitions are semantically equivalent. The necessary conditions for semantic equivalence
of functional expressions are discussed with respect to various functional closures of the basic set of
function symbols using the case of real-valued functions of real variables.