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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 specificationbuilding 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

Cited by 66 (14 self)
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The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specificationbuilding 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.
Relating CASL with Other Specification Languages: the Institution Level
, 2000
"... In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEPtheories, as well as various sublanguages of Casl that more or ..."
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Cited by 37 (16 self)
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In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEPtheories, as well as various sublanguages of Casl that more or less directly correspond to these. All these languages are translated to an appropriate sublanguage of Casl. The translation mainly concerns the level of specification inthesmall: the logics underlying the languages are formalized as institutions, and representations among the institutions are developed. However, it is also considered how these translations interact with specification inthelarge. Thus, we obtain one hand translations of any of the abovementioned specification languages to an appropriate sublanguage of Casl. This allows us to take libraries and case studies that have been developed for other languages and reuse them in Casl. On the other hand, we set up institution repre...
Some Thoughts on Algebraic Specification
 PROC. 3RD WORKSHOP ON THEORY AND APPLICATIONS OF ABSTRACT DATA TYPES
, 1985
"... ..."
On Observational Equivalence and Algebraic Specification (Extended Abstract)
, 1984
"... The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specificationbuilding 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 specificationbuilding 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.
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