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Programming in the Geometric Machine

This paper presents the programming language induced by the ordered structure of the Geometric Machine Model (GMM). 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. Using the programming language induced by such structure, simple recursive equations and related algorithms are presented, and their domain-theoretic semantics in the machine model is given.