We present a report on work in progress on certain aspects of a programme of research concerned with building formal, mathematical models both for aspects of the computational process and for features of programming languages. In this paper, considering work of Kozen showing that complete normed vector spaces (Banach spaces) and bounded linear operators provide a framework for the semantics of deterministic and probabilistic programs, we include logic programs within this framework. We thereby make it a framework in which it is possible to handle the semantics of all three types of program. Using these ideas, we advance a programme of research proposed by M. Bukatin and J.S. Scott concerned with defining and computing meaningful notions of metrics and generalized metrics measuring the distance between two programs, the terms metrics and generalized metrics being used here in the precise sense in which they are employed in mathematics. The longterm objective of this work is to use such metrics as tools in measuring correctness of programs.