Global Syntax and Semantics for Recursively Enumerable Languages

Abstract

According to (Benson, 1970), a syntax is a category of strings and derivations (modulo similarity) between them. In this paper the semantic domain is an elementary topes. Thus, an interpretation of a syntax is a cofunctor taking strigs to products and derivations to morphisms. It is proved the existence of a free x – category $\mathcal{U}$ such that every syntax is a full subcategory of $\mathcal{U}$ , which can be determined recursively. Every interpretation of a syntax is the restriction of the interpretation of $\mathcal{U}$ .