Universal algebra in higher types
In this highly readable paper, the author outlines applications of the elementary theory of higher-type universal algebra to the theory of computation. The underlying motif is the application of abstract ideas of many-sorted universal algebra (in the sense of, e.g., \textit{P. M. Cohn's} book on universal algebra [Universal algebra (1965; Zbl 0141.010)] to theoretical computer science. The important role of recursivity in the computational aspects of the algebraic techniques is not clear to this reviewer; i.e., one is neither developing a recursive category theory nor a recursive universal algebra. A useful completeness theorem is proved. Further, there are interesting discussions of extensions of G. Birkhoff's Variety Theorem and A. I. Mal'tsev's Quasivariety Theorem.
applications of the elementary theory of higher-type universal algebra to the theory of computation
scientific article; zbMATH DE number 96048
scientific article