Some new properties of lists and a framework of a list theoretic relation model

The concept of list is of very much importance in the field of computer science as a data structure [6] and in programming languages like LISP [7]. The concept was redefined by Jena, Tripathy and Ghosh [10] in 2001, in an attempt to introduce it as an extension of the concept of characteristic function for sets and count function for multisets. Since then, many concepts related to list theory have been introduced from the new angle and many properties are established ([11], [12] and [13]). In this paper, we continue this effort and define three new concepts of filter, zip* and indexlist. We establish many properties of these notions. Particularly, the concept of filter is of enough importance and interest. It has many applications in array manipulation in data structure [1, 4, 8] and query realization from databases [5, 14]. We propose the design of a list theory based relational database model using position function approach and illustrate how query processing can be realized for the relational algebraic operation of 'Selection' on it, using the 'filter' operation.