A Programming Language for the Interval Geometric Machine

This paper presents an interval version of the Geometric Machine Model (GMM) and the programming language induced by its structure. The GMM is an abstract machine model, based on Girard’s coherence space, capable of modelling sequential, alternative, parallel (synchronous) and non-deterministic computations on a (possibly infinite) shared memory. The processes of the GMM are inductively constructed in a Coherence Space of Processes. The memory of the GMM, supporting a coherence space of states, is conceived as the set of points of a three dimensional euclidian space. The version of the GMM presented here operates with real intervals, and is defined to model the semantics of algorithms of Interval Mathematics. Using the programming language induced by such structure, simple interval algorithms are presented, and their domain-theoretic semantics in the machine model is given.