On proving the correctness of data type implementations

In order to prove the correctness (or consistency) of an implementation of a data type with respect to the data type's specifications, the minimal amount of information that needs to be provided consists of: (i) a specification of the type being implemented; (ii) a specification of the representation type; and (iii) a specification of an implementation. This paper develops a method for proving the correctness of data type implementations that requires only this minimal amount of information to be specified in order for a proof to be attempted; this is in contrast to several of the existing methods which need additional information augmenting (i)-(iii) to be specified in order to be applicable. The ensuing generality of the proposed method makes it more amenable to automation. Examples of applications of the proof method are presented, all of which have been automated.