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Global Syntax and Semantics for Recursively Enumerable Languages

Cristian S. Calude, Gheorghe Pǎun

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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 U such that every syntax is a full subcategory of U, which can be determined recursively. Every interpretation of a syntax is the restriction of the interpretation of U.

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What this paper is about

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 U such that every syntax is a full subcategory of U, which can be determined recursively. Every interpretation of a syntax is the restriction of the interpretation of U.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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 U such that every syntax is a full subcategory of U, which can be determined recursively. Every interpretation of a syntax is the restriction of the interpretation of U.

Key concepts: Syntax, Interpretation (philosophy), Abstract syntax, Semantics (computer science), Morphism, Computer science, Abstract interpretation, Programming language

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