The declarative past and imperative future

Abstract

We propose a new paradigm in executable logic, that of the declarative past and imperative future. A future statement of temporal logic can be understood in two ways: the declarative way, that of describing the future as a temporal extension; and the imperative way, that of making sure that the future will happen the way we want it. Since the future has not yet happened, we have a language which can be both declarative and imperative. We regard our theme as a natural meeting between the imperative and declarative paradigms.

More specifically, we describe a temporal logic with Since, Until and fixed point operators. The logic is based on the natural numbers as the flow of time and can be used for the specification and control of process behaviour in time. A specification formula of this logic can be automatically re-written into an executable form. In an executable form it can be used as a program for controlling process behaviour. The executable form has the structure “If A holds in the past then do B”. This structure shows that declarative and imperative programming can be integrated in a natural way.

This research was supported by the Science and Engineering Research Council under grant GR/D/5939.7 as part of the ALVEY project “Pure Logic Language” IKBS/170, and by the National Science Foundation under grant IST-8505586. I would like to thank Ian Hodkinson and Richard Owens for carefully reading the draft, making many suggestions and helping with the preparation of this paper. Any errors, naturally, remain the responsibility of the author.