The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specification-building operation are studied. We begin with a defmition of observational equivalence which is adequate to handle reachable algebras only, and show how to extend it to cope with unreachable algebras and also how it may be generalised to make sense under an arbitrary institution. Behavioural equivalence is treated as an important special case of observational equivalence, and its central role in program development is shown by means of an example.

The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system used to write specifications, building on Goguen and Burstall's work on the notion of an institution as a formalisation of the concept of a logical system. One advantage of this is that it permits freedom in the choice of the logic used in writing specifications; an intriguing side-effect is that it enables Extended ML to be used to develop programs in languages other than Standard ML since we view programs as simply Extended ML specifications which happen to include only "executable" axioms. The semantics of Extended ML is defined in terms of the primitive specification-building operations of the ASL kernel specification language which itself has an institution-independent semantics. It is no...

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A formalisation of this programming methodology depends on some precise notion of the implementation of a specification by a lower-level specification. Previous notions have been given for the implementation of non-parameterised ([GTW 78], [Nou 79], [Hup 80], [EKP 80], [Ehr 82]) and parameterised ([Gan 81], [Hup 81])*~ specifications, but none of these approaches deals fully with 'structured ' algebraic specifications (as in Clear [BG 77] or CIP-L [Bau 81]) which may be constructed in a hierarchical fashion and may be loose (with an assortment of non-isomorphic models). We present a definition of implementation which agrees with our intuitive notions built upon programming experience and which handles such loose hierarchical specifications, based on a new (and seemingly fundamental) concept of the simulation of a theory by an algebra. We show how this definition extends to give a definition of the implementation of parameterised specifications. An example of an implementation is given and several other examples are sketched. We work within the framework of the Clear specification language [BG 77] which allows large specifications to be built from small easy-to-understand bits. For most