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On Observational Equivalence and Algebraic Specification
, 1987
"... 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 wit ..."
Abstract
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Cited by 66 (17 self)
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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.
Some Thoughts on Algebraic Specification
- PROC. 3RD WORKSHOP ON THEORY AND APPLICATIONS OF ABSTRACT DATA TYPES
, 1985
"... ..."
Chapter 1 SPECIFICATION SEMANTICS
"... X s , and t 1 : : : t n f 2 jT \Sigma (X)j s for all f : s 1 \Theta : : : \Theta s n ! s in \Sigma and t 1 2 jT \Sigma (X)j s1 ; : : : ; t n 2 jT \Sigma (X)j sn . The interpretation of an operation name becomes now the appending of the operation name at the end of the argument sequence. This represe ..."
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X s , and t 1 : : : t n f 2 jT \Sigma (X)j s for all f : s 1 \Theta : : : \Theta s n ! s in \Sigma and t 1 2 jT \Sigma (X)j s1 ; : : : ; t n 2 jT \Sigma (X)j sn . The interpretation of an operation name becomes now the appending of the operation name at the end of the argument sequence. This representation of terms is sometimes called postfix polish notation. This is a very compact representation of terms without any technical symbols and very useful for evaluating terms by means of a stack machine. But for a human reader this prototype algebra of terms is not very convenient. Human readers prefer the representation with technical symbols, as in Section 2.4, which represents in a better way the tree like structure of terms. Using a class of algebras opens the possibility to define the class axiomatically, where the axioms express the characteristic properties ensuring the same external behavior of all algebras in the class. In the following we will investigate what precise kinds of
ON OBSERVATIONAL EQUIVALENCE AND ALGEBRAIC SPECIFICATION-- Extended abstract i--
"... 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 ..."
Abstract
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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. 1
