Abstract
“Observational specifications” are presented in order to provide a concept for determining the observable parts of algebraic specifications. Syntactically, equational specifications are extended to contain an “observability predicate” which allows to specify the “observable terms”. Semantically, a notion of “observational homomorphism” respectively “full observational homomorphism” respecting only the observable objects of algebras is introduced.
A syntactic criterion is given for characterizing those classes of algebras which are closed under observational isomorphism. As a consequence a Birkhoff-like theorem can be proved which shows that any class of algebras closed under the formation of products, subalgebras and full observational homomorphism can be specified by a set of “observable” equations and observations. Vice versa, (the class of models of) any specification specified by a set of “observable” equations and observations is closed under the formation of products, subalgebras and full observational homomorphism.
This work has been partially sponsored by the ESPRIT-project METEOR
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Hennicker, R., Wirsing, M. (1985). Observational Specification: A Birkhoff-Theorem. In: Kreowski, HJ. (eds) Recent Trends in Data Type Specification. Informatik-Fachberichte, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09691-8_10
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DOI: https://doi.org/10.1007/978-3-662-09691-8_10
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