Presenting functors on many-sorted varieties and applications

Authors:
Alexander Kurz;Daniela Petrişan
Affiliations:
Department of Computer Science, University of Leicester, UK;Department of Computer Science, University of Leicester, UK
Venue:
Information and Computation
Year:
2010

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Abstract

This paper studies several applications of the notion of a presentation of a functor by operations and equations. We show that the technically straightforward generalisation of this notion from the one-sorted to the many-sorted case has several interesting consequences. First, it can be applied to give equational logic for the binding algebras modelling abstract syntax. Second, it provides a categorical approach to algebraic semantics of first-order logic. Third, this notion links the uniform treatment of logics for coalgebras of an arbitrary type T with concrete syntax and proof systems. Analysing the many-sorted case is essential for modular completeness proofs of coalgebraic logics.