Abstract

A general theory of computing is important, if we wish to have a common mathematical footing based on which diverse scienti c and engineering eorts in computing are uniformly understood and integrated. A quest for such a general theory may take dierent paths. As a case for one of the possible paths towards a general theory, this paper establishes a precise connection between a game-based model of sequential functions by Hyland and Ong on the one hand, and a typed version of the -calculus on the other. This connection has been instrumental in our recent eorts to use the -calculus as a basic mathematical tool for representing diverse classes of behaviours, even though the exact form of the correspondence has not been presented in a published form. By redeeming this correspondence we try to make explicit a convergence of ideas and structures between two distinct threads of Theoretical Computer Science. This convergence indicates a methodology for organising our understanding on computation and that methodology, we argue, suggests one of the promising paths to a general theory.

Citations