The gradual process of data abstraction

In this paper we present the gradual process of building abstract data types (ADTs), such as Fractions and Polynomials. They are built from basic ADTs, such as Booleans and Integers. We propose a set of functional categories in order to classify ADT functions. These functions are stated in functional programming, that is without using variable assignment, sequence, or loops. Functions stated in this way to accomplish the simplification task of an Integer and to get an ordered sum for a Polynomial are not reported in literature so far. We also point to the inherent relation between ADT functions and operator overloading.