Abstract
The aim of the paper is to present the operational semantics of Algebraic Abstract Data Types (AAT) in terms of rewriting systems and their programming in PROLOG respectively.
An AAT is considered as an interpretor, the semantical actions of which are rewrite rules.
The power of the methodology makes it possible to construct one and many-sorted types, and may be used as an aid for proofs of properties.
This approach leads to a clean, rapid, and accurate programming close to the abstract specification of the type. Proofs by "constructor induction" or Knuth-Bendix algorithm of equational properties valid in initial or final models may be programmed in PROLOG.
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Références
A.L. FURTADO, P.A.S. VELOSO Procedural Verification and Implementations for Abstract Data Types, Pontificia Universidade Catolica do Rio de Janeiro. Private communication.
M.C. GAUDEL Compiler Proof and Generation based on semantics of programming Languages (French) Thèse de Doctorat — 10 th March 1980 — Nancy —
J.A. GOGUEN. How to prove algebraic inductive hypotheses without induction with applications to the correctness of data type implementation. 5th Conference on Automated Deduction. Les Arcs, France, Juillet 1980. (LNCS 87, pp. 356–373).
J.A. GOGUEN, J.J. TARDO, "An introduction to OBJ, A Language for writing and testing Formal Algebraic Program Specification". Specification of Reliable Software. Boston Apr. 1979. pp. 170–189.
J.V. GUTTAG, J.J. HORNING, The Algebraic Specification of Abstract Data Types. Acta Informatica 10 (1978), 27–52.
J. GUTTAG Abstract Data Types and the Development of Data Structures. CACM — V20 — N6 — June 1977 — pp 396–404.
G. HUET, J.M. HULLOT, Proofs by Induction in Equational Theories with Constructors. Rapport INRIA no28.
G. HUET, D. OPPEN Equations and Rewrite Rules: a Survey. "Formal Languages: Perspectives and Open Problems". Ed. Book R, Academic Press 1980. Also TR-CSL-111, SRI International, Jan. 1980.
E. MADELAINE, S. SENESI, On using LCF and PROLOG to prove Correctness of Abstract Data Type Representation (French). Ecole Polytechnique — INRIA — July 1980.
D.R. MUSSER "A Data Type Verification System Based on Rewrite Rules". Proceedings of the Sixth Texas Conference
D.R. MUSSER, Convergent Set of Rewrite Rules for Abstract Data Types. USC — ISI. Californie. Déc. 78 — Nov. 79.
C. PAIR On the Models of Algebraic Abstract Data Types (French) Centre de Recherche en Informatique de Nancy — Report 80 P 052, May 1980.
P. ROUSSEL PROLOG Reference Manual (French) Université d'Aix — Marseille II — Septembre 1975.
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© 1981 Springer-Verlag Berlin Heidelberg
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Bergman, M., Deransart, P. (1981). Abstract data types and rewriting systems : Application to the programming of Algebraic Abstract Data Types in PROLOG. In: Astesiano, E., Böhm, C. (eds) CAAP '81. CAAP 1981. Lecture Notes in Computer Science, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10828-9_57
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DOI: https://doi.org/10.1007/3-540-10828-9_57
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