## Algebra of Normal Function Tables

Dr. Martin von Mohrenschildt

Software Engineering Research Group

CRL, McMaster University,

Hamilton, Ontario, Canada L8S 4K1

### Abstract

In contrast to classical algebra and analysis the functions encountered
in computer science are usually piecewise continuous functions or functions
whose evaluation rules change dramatically depending on a subset of the
input values. Because of the pervasiveness of the if-then-else construction
in programming, we have to extend classical mathematical methods to handle
this kind of object. We approach this class of functions using tabular
expressions. In this paper we define a function algebra, over a many sorted
algebra, which is closed under composition. Then, this function algebra is
extended to tables. This enables us to define the composition of tables.
We show that this algebra of tables is closed under composition.
We give two algorithms to compute the composition of tables.