Interaction categories and the foundations of typed concurrent programming

We propose Interaction Categories as a new paradigm for the semantics of functional and concurrent computation. Interaction categories have speciications as objects , processes as morphisms, and interaction as composition. We introduce two key examples of interaction categories for concurrent computation and indicate how a general axiomatisation can be developed. The upshot of our approach is that traditional process calculus is reconstituted in functorial form, and integrated with type theory and functional programming. A second contribution of the paper is to propose a way of combining the Propositions-as-Types and Veriication paradigms based on the notion of Speciication Structure. We describe speciication structures for liveness properties and deadlock-freedom, and illustrate our ideas using a standard example from concurrency theory.

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