Nets over many sorted operator domains and their semantics

Abstract

In this paper is given a rigorous framework for the description of syntax, behaviour and semantics in the general case of many sorted operator domains, i.e. not only in the case describing the underlying syntax structure by trees.

Given a many sorted operator domain ω, a syntax description is yielded by an ω-net ψ : V → (V+X) ω, that is an object of the category ω-net. Any ω-algebra may be taken as a "processor". Let Beh be an appropriate behaviour category, we get the semantics as a bifunctor

$$Sem:\underline {\Omega - net} ^{op} \times \underline {\Omega - alg} \to \underline {Beh} .$$

A partially defined binary composition * for objects in ω-net such as in Beh is given and it is shown, that Sem preserves these compositions.