Algebraic Implementation of Abstract Data Types: Concept, Syntax, Semantics and Correctness

A new concept for the implementation of abstract data types is proposed: Given algebraic specifications SPECO and SPEC1 of abstract data types ADTO and ADT1 an implementation of ADTO by ADT1 is defined separately on the syntactical level of specifications and on the semantical level of algebras. This concept is shown to satisfy a number of conceptual requirements for the implementation of abstract data types. Several correctness criteria are given and illustrating examples are provided.