On algorithmic theory of stacks

  • Andrzej Salwicki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 64)


Algorithmic Theory of Stacks ATS formalizes properties of relational systems of stacks. It turns out that apart of previously known axioms, the new axiom of algorithmic nature [while - empty(s)do s := pop(s)]true is in place. The representation theorem stating that every relational system of stacks is isomorphic to a system of finite sequences of elements is proved. The connections between ATS and a type STACKS declaration /written in LOGLAN programming language/ are shown.


Relational System Binary Search Tree Algorithmic Logic Algorithmic Theory Abstract Data Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Banachowski, L., An axiomatic approach to the theory of data structures, Bull.Acad.Pol.Ser.Math.Phys.Astr. 23 1975, 315–323Google Scholar
  2. [2]
    Grabowski, M., On relationship between algorithmic logic and full weak second order logic /in polish/, 1977, University of Warsaw, unpublished manuscriptGoogle Scholar
  3. [3]
    Guttag, J., Abstract Data Types... CACM 20 1977, 396–404Google Scholar
  4. [4]
    Liskov, B.M., Zilles, S.N., Programming with abstract data types Proc. ACM SIGPLAN Symp. on Very High Level Lang. SIGPLAN Notices ACM 9, 4 1974, 50–59Google Scholar
  5. [5]
    Mirkowska, G., Algorithmic logic and its applications in program theory, Fundamenta Informaticae 1 1977, 1–17, 147–167Google Scholar
  6. [6]
    Salwicki, A., Applied algorithmic logic, Proc. MFCS'77 inLect. Notes in Comp.Sci. 53, Springer Verlag, 1977, 122–134Google Scholar
  7. [7]
    Spitzen, J., Wegbreit, B., The verification and synthesis of data structures, Acta Inf. 4 1975, 127–144CrossRefGoogle Scholar
  8. [8]
    Goguen, J.A., Thatcher, J.W., Wagner, E.G., An initial algebra approach to the specification, correctness and implementation of abstract data types, in Current Trends in Programming Methodology 4, ed by R.YehGoogle Scholar
  9. [9]
    Tue, Nguen, A comparison of different implementations of dictionary and priority queue theories, in polish, University of Warsaw, 1978Google Scholar
  10. [10]
    Salwicki, A., On Algorithmic theory of stacks, to appear in Fundamenta InformaticaeGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Andrzej Salwicki
    • 1
  1. 1.Mathematical Institute PASWarsaw

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