Algebraic specifiability of data types with minimal computable parameters (Q1183572)

A necessary and sufficient condition for the existence of an algebraic specification for parametrized data types whose domain consists of all the semicomputable algebras in some quasi-variety was established by \textit{J. A. Bergstra} and \textit{J. W. Klop} [Automata, languages and programming, 9th Colloq., Aarhus/Den. 1982, Lect. Notes Comput. Sci. 140, 23-24 (1982; Zbl 0489.68016); Elektron. Informationsverarbeitung Kybernetik 19, 17-31 (1983; Zbl 0516.68019)]. A similar work is done with persistent parametrized data types whose parameters come from certain classes of computable data types. It is shown that for minimal algebras and under certain assumptions on the domain of parameters a persistent parametrized data type with computable parameters is effective iff it has a finite equational specification.