Model theoretic aspects of abstract data specification
Alberto Bertoni, Giancarlo Mauri, Pierangelo Miglioli · BOA (University of Milano-Bicocca) · 1979
The thesis is that an abstract data type is a model of a set of axioms which is both initial and prime; initiality is to be connected with the constructive operations, primeness with the algorithmic ones. In a sense the prime model gives a characterization of the maximal set of objects one can describe. Finally, the authors introduce the notion of m-completeness of a theory, and show how by requiring this property for the abstract model one can guarantee that all the formulas holding on this model hold also on all the `concrete' representation.