Conceptual Application of List Theory to Data Structures

Abstract

Following the approach of defining a set through its characteristic function and a multiset (bag) through its count function, Tripathy, Ghosh and Jena ([3]) introduced the concept of position function to define lists. The new definition has much rigor than the earlier one used in computer science in general and functional programming ([2]) in particular. Several of the concepts in the form of operations, operators and properties have been established in a sequence of papers by Tripathy and his coauthors ([3, 6, 7, 8]. Also, the concepts of fuzzy lists ([4]) and that of intuitionistic fuzzy lists ([5]) have been defined and studied by them. Recently an application to develop list theoretic relational databases and operations on them has been put forth by Tripathy and Gantayat ([9]). In the present article we provide another application of this approach in defining data structures like Stack, Queue and Array. One of the major advantages of this approach is the ease in extending all the concepts for basic lists to the context of fuzzy lists and intuitionistic fuzzy lists. We also illustrate this approach in the present paper.