Abstract
We introduce a concept of behavioural implementation for algebraic specifications which is based on an indistinguishability relation (called behavioural equality). The central objective of this work is the investigation of proof rules that first allow us to establish the correctness of behavioural implementations in a modular way and moreover are practicable enough to induce proof obligations that can be discharged with existing theorem provers. Our proof technique can also be applied for proving abstractor implementations in the sense of Sannella and Tarlecki.
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G. Bernot, M. Bidoit: Proving the correctness of algebraically specified software: modularity and observability issues. Proc. AMAST '91, 216–242, Springer-Verlag Workshops in Computing Series, 1992.
M. Bidoit, R. Hennicker: Proving ehavioural theorems with standard first-order logic. In Proc. ALP '94, Fourth International Conference on Algebraic and Logic Programming, Springer Lecture Notes in Computer Science 850,41–58,1994.
M. Bidoit, R. Hennicker. Behavioural theories and the proof of behavioural properties. Report LIENS-95-5, Ecole Normale Supérieure, 1995.
M. Bidoit, R. Hennicker: Proving the correctness of behavioural implementations. Technical Report, Universität München, 1995.
M. Bidoit, R. Hennicker, M. Wirsing: Behavioural and abstractor specifications. Report LIENS-94-10, Ecole Normale Supérieure, 1994. Revised version to appear in Science of Computer Programming.
H. Ehrig, B. Mahr: Fundamentals of algebraic specification 1, EATCS Monographs on Theoretical Computer Science 6, Springer, 1985.
J. Guttag, J. Horning: Larch: Languages and Tools for Formal Specification. Texts and Monographs in Computer Science, Springer, 1993.
J. A. Goguen, J. Meseguer: Universal realization, persistent interconnection and implementation of abstract modules. In Proc. ICALP '82, Springer Lecture Notes in Computer Science 140, 265–281,1982.
C. A. R. Hoare: Proofs of correctness of data representations. Acta Informatica 1, 271–281,1972.
G. Kreisel, J. L. Krivine: Eléments de Logique Mathematique. Dunod (Paris), 1967.
P. Nivela, F. Orejas: Initial behaviour semantics for algebraic specifications. In: D. T. Sannella, A. Tarlecki (eds.): Proc. 5th Workshop on Algebraic Specifications of Abstract Data Types, Springer Lecture Notes in Computer Science 332, 184–207, 1988.
H. Reichel: Initial computability, algebraic specifications, and partial algebras. International Series of Monographs in Computer Science No. 2, Oxford: Clarendon Press, 1987.
O. Schoett: Data abstraction and correctness of modular programming. Ph. D. thesis, CST-42-87, University of Edinburgh, 1987.
D. T. Sannella, A. Tarlecki: Toward formal development of programs from algebraic specifications: implementation revisited. Acta Informatica 25, 233–281, 1988.
M. Wirsing: Algebraic specification. In: J. van Leeuwen (ed.): Handbook of Theoretical Computer Science, 675–788, Elsevier Science Publishers B. V., 1990.
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Bidoit, M., Hennicker, R. (1995). Proving the correctness of behavioural implementations. In: Alagar, V.S., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1995. Lecture Notes in Computer Science, vol 936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60043-4_51
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DOI: https://doi.org/10.1007/3-540-60043-4_51
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