Abstract
We are arguing that main problems of data structures i.e.
-
specification,
-
implementation,
-
verification,
can be approached and solved by developping and studying theories of data structures which are based on algorithmic logic AL. we propose to specify a data structure by a proper set of algorithmic axioms. Then verification of a corresponding property of a program consists in proving the formula which expresses the property. The proof making use of axioms of the data structure.
We present a case study of the algorithmic theory of priority queues ATPQ. we show that the axiomatization of ATPQ is proper by proving the representation theorem, Namely, every model of the theory is isomorphic with the two-sorted model of a linearly ordered set of elements and the family of all finite subsets of the given set of elements, Next, we prove the correctness of an implementation of priority queues in binary search trees. We relate theoretical results to corresponding modules of software written in LOGLAN programming language. Remarks on dynamization of abstract theories of data structures by adding notion of reference, also axiomatizable in AL, are given. Finally, we compare our approach with others known in the literature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho,A., Hopcroft,J., ullman,J., The design and analysis of computer algorithms, Addiaon-Wesley, 1974
Banachowski,L., On proving program correctness by means of stepwise refinement method, to appear in Proc. Symp. Algorithmic Logic and LOGLAN in Lecture Notes in Computer Science
Bartol,W.M.,et al., Report on the LOGLAN programming language Müldner, T., ed University of Warsaw 1981
Dańko,W., A criterion of undecidability of algorithmic theories, in Proc. MFCS'80 P.Dembinski ed. LNCS Springer Vlg vol.88
Engeler,E., Algorithmic properties of structures, Math. Systems Theory 1 (1967), 183–195
Goguen,J. A.,Thatcher,J.W., Wagner,E.G., An initial algebra approach to the specification, correctness and implementation of abstarct data types, IBM Rep. RC 6487(1977)
Guttag,J., Abstract data types... CACM 20 (1977), 396–404
Hoare,C.A.R., Proof of correctness of data representation, Acta Informatica 1 (1972), 271–281
Kfoury.D., Comparing algebraic structures up to algorithmic equivalence in Proc 1-st ICALP'72. North-Holland 1972
Kreczmar,A., Programmability in fields, Fundamenta Informaticae 1 (1977), 195–220
Knuth,D., The art of computer programming, vol.3 Addison-Wesley 73
Liskov,B.M., Zilles,S.N., Programming with abstract data types Proc ACM SIGPLAN Symp. on Very High Level languages, SIGPLAN Notices 4 (1974), 50–59
Mazur,S., Computable analysis, Dissertationes Mathematicae 33 (1963 PWN)Publ. Warsaw
Mirkowska, G., Algorithmic logic and its applications in the theory of programs, Fundamenta Informaticae 1 (1977), 1–17, 147–167
Mirkowska, G.,Algorithmic logic with nondeterministic programs, Fundamenta informaticae 1 (1980), 45–64
OKtaba.H., un algorithmic theory of reference, Ph.D. Thesis university of Warsaw 1981
Salwicki, A., On algorithmic theory of stacks in Proc.MFCS78 J.Winkowski ed. Lecture Notes in Comp.Sci. v. 64, 452–461
Salwicki,A., On the algorithmic theory of dictionaries, in Proc Logic of Programs E. Engeler ed. LNCS vol.125, 145–168
Scott,D., Data types as lattices, SIAM J.Comp. 5(1976), 522–587
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Salwicki, A. (1982). Algorithmic theories of data structures. In: Nielsen, M., Schmidt, E.M. (eds) Automata, Languages and Programming. ICALP 1982. Lecture Notes in Computer Science, vol 140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012792
Download citation
DOI: https://doi.org/10.1007/BFb0012792
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11576-2
Online ISBN: 978-3-540-39308-5
eBook Packages: Springer Book Archive