Behavioural specifications

Abstract

We now consider how the material in the preceding chapters must be adapted when we take a behavioural view of specifications, whereby the “behaviour” of an algebra is fully determined by the results delivered by term evaluation. However, only results of certain observable sorts can be directly observed, with two algebras being behaviourally equivalent with respect to the observable sorts if evaluating terms of observable sort always produces the same result in both algebras. This is the essential idea behind data abstraction: we encapsulate a data type together with operations to be used by a client, hiding the actual data representation and any representation-level operations. Then different representations that exhibit the same behaviour can be used interchangeably. Arguably, specifications should not distinguish between algebras that are behaviourally equivalent, which may be ensured by explicitly closing the class of models of a specification under behavioural equivalence. An alternative is to relax the interpretation of equality in sentences so that indistinguishable values of non-observable sorts are regarded as equal.