# On observational equivalence and algebraic specification

Extended abstract

Colloquium On Trees In Algebra And Programming Specifications

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## Abstract

The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specification-building operation (observational abstraction) are studied. We begin with a definition 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.

## Keywords

Abstract Data Type Signature Morphism Algebraic Specification Springer LNCS Infinitary Logic
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