Abstract
An observational notion of implementation for algebraic specifications is presented which formalizes the intuitive idea that an implementation is correct if it produces correct observable output. Based on a theory of observational specifications proof theoretic criteria for implementation relations are provided and a proof technique (called "context induction") for the verification of observational implementation relations is presented. As an example an abstract specification of (the algebraic semantics of) a small imperative programming language is implemented by a state oriented specification of the language.
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M. Broy, C. Pair und M. Wirsing: A systematic study of models of abstract data types. Theoretical Computer Science 33, 139–174 (1984).
M. Broy, P. Pepper und M. Wirsing: On the algebraic definition of programming languages. ACM Trans. on Prog. Languages and Systems 9, 1, 54–99 (1987).
P.M. Cohn: Universal algebra. D. Reidel Publishing Company, Dordrecht, Holland (rev. edition), (1981).
H. Ehrig, H.J. Kreowski, B. Mahr und P. Padawitz: Algebraic implementation of abstract data types. Theoretical Computer Science 20, 209–263 (1982).
V. Giarratana, F. Gimona und U. Montanari: Observability concepts in abstract data type specification. In: A. Mazurkiewicz (ed.): Proc. MFCS 76, 5th Internat. Symp. on Mathematical Foundations of Comp. Science, Gdansk, Sept. 1976. Springer Lecture Notes in Computer Science 45, 576–587 (1976).
J.A. Goguen, R.M. Burstall: CAT, a system for the structured elaboration of correct programs from structured specifications. Technical report CSL-118, Comp. Science Laboratory, SRI International (1980).
J.A. Goguen, J. Meseguer: Universal realization, persistent interconnection and implementation of abstract modules. In: M. Nielsen, E.M. Schmidt (eds.): Proc. ICALP 82, 9th Coll. on Automata, Languages and Programming, Aarhus, July 1982. Springer Lecture Notes in Computer Science 140, 265–281 (1982).
R. Hennicker: Beobachtungsorientierte Spezifikationen. Dissertation, Fakultät für Mathematik und Informatik, Universität Passau (1988).
R. Hennicker, M. Wirsing: Observational specification: a Birkhoff-theorem. In: H.J. Kreowski (ed.): Recent Trends in Data Type Specification. 3rd Workshop on Theory and Appl. of Abstract Data Types, Selected Papers. Informatik Fachberichte 116, 119–135, Springer Verlag (1985).
H. Reichel: Behavioural equivalence — a unifying concept for initial and final specification methods. In: M. Arato, L. Varga (eds.): Math. Models in Comp. Systems, Proc. 3rd Hungarian Computer Science Conf., Budapest, January 1981, 27–39 (1981).
D.T. Sannella, A. Tarlecki: On observational equivalence and algebraic specification. In: H. Ehrig, C. Floyd, M. Nivat, J. Thatcher (eds.): Proc. TAPSOFT 85, Joint Conf. on Theory and Practice of Software Development, Berlin, March 1985. Springer Lecture Notes in Computer Science 185, 308–322 (1985).
D.T. Sannella, A. Tarlecki: Toward formal development of programs from algebraic specifications: implementations revisited. Proc. TAPSOFT 87, Joint Conf. on Theory and Practice of Software Development, Pisa, March 1986. Springer Lecture Notes in Computer Science 249, 96–110 (1987).
D.T. Sannella, M. Wirsing: Implementation of parameterized specifications. In: M. Nielsen, E.M. Schmidt (eds.): Proc. ICALP 82, 9th Coll. on Automata, Languages and Programming, Aarhus, July 1982. Springer Lecture Notes in Computer Science 140, 473–488 (1982).
O. Schoett: Data abstraction and the correctness of modular programming. Ph.D. thesis, CST-42-87, Department of Comp. Science, University of Edinburgh (1987).
A. Selman: Completeness of calculi for axiomatically defined classes of algebras. Algebra universalis 2, 20–32 (1972).
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© 1989 Springer-Verlag Berlin Heidelberg
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Hennicker, R. (1989). Observational implementations. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028973
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DOI: https://doi.org/10.1007/BFb0028973
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