An outline of a mathematical model for the definition and manipulation of data

Abstract

This paper presents a constructive model for data which suggests some precise definitions of notions like type, name, constants, declarations etc. The model is based on an old idea of looking at data as a mapping from a set of names to a set of values. We will study two different kinds of assignments and also show how the model can be used to give some hints for new data structuring methods. In particular we have given a definition of a sequence and we have shown how this data structure can be used to give constructive definitions of structures like stacks, files and queues. We have also studied tree traversals i.e. the correspondence between various trees and sequences.