Procedural implementation of algebraic specification

An implementation of an algebraic specification in an imperative programming language consists of a representation type, together with an invariant and an equivalence relation over it, and a procedure for each operator in the specification. A formal technique is developed to check the correctness of an implementation with respect to its specification. Here “correctness” means that the implementation satisfies the axioms and preserves the behavior of the specification. Within legal representing value space, a correct implementation behaves like a desirable model of the specification. A notion of implementation refinement is also proposed, and it is shown that the correctness relation between implementations and specifications is preserved by implementation refinement. In the extreme case the procedures in an implementation may be pre-post-condition pairs. Such abstract implementations can be refined into executable code by refining the abstract procedures in it. In this way a formal link between the algebraic and the pre- post-condition specification techniques is established.

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