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Quasi-varieties in abstract algebraic institutions. (English) Zbl 0622.68033
The author specializes the extremely general notion of institution introduced by J. A. Goguen and R. M. Burstall [Lect. Notes Comput. Sci. 164, 221-256 (1984; Zbl 0543.68021)] to obtain his own notion of abstract algebraic institution. It is shown that in abstract algebraic institutions quasi-varieties and strict quasi-varieties are characterized respectively as implicational and strict implicational classes. This allows the author to present characterizations of the most general algebraic institution which strongly admit initial semantics [cf. A. Tarlecki, Theor. Comput. Sci. 37, 269-304 (1985; Zbl 0608.68014)] in more standard syntactical terms. These general considerations are applied to three familiar classes of total, partial and continuous algebras.
Reviewer: H.Nishimura

68Q65 Abstract data types; algebraic specification
68P05 Data structures
Full Text: DOI
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