Proving programs by sets of computations

  • A. Blikle
Theory Of Programs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 28)


By a computation of a program we mean any finite or infinite sequence of consecutive data-vector states generated by the program during a run. The set of all such computations can be considered as the program meaning. Analysing programs by sets of computations permits one to deal not only with input-output properties like correctness or termination, but also with properties of runs independently are they finite or not. In particular one can analyse system-like programs, where no output at all is expected. Given a program to be analysed we split it into a finite number of modules each of them simple enough for the set of all its computations to be obvioust. Sets of computations associated to modules are combined then into a global set in a way that is described by operational semantics. This semantics — being of litle use for program analysis — is supplemented then by a fixed point semantics that is proved equivalent to the former. Two examples of program analysis are considered: the McCarthy's 91-procedure and a consumer-producer system-like program.

Key words and phrases

recursive procedure set of computations algebra of computations operational semantics fixed point semantics least fixed point greatest fixed point deadlock 

Category numbers

CR 5.24 AMS(MOS) 68A05 06A23 


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  1. [1]
    BLIKLE, A. Nets, complete lattices with a composition. Bull. Acad. Polon. Sci., Ser. Sci. Mathemat. Astronom. Phys. 19(1971), 1123–1127Google Scholar
  2. [2]
    BLIKLE, A. Equations in nets — computer oriented lattices. CC PAS Reports 99(1973)Google Scholar
  3. [3]
    BLIKLE, A. An algebraic approach to programs and their computations. Math. Found. Comp. Sci. II (Proc. Symp. High Tatras, 1973) pp. 17–26. High Tatras 1973Google Scholar
  4. [4]
    BLIKLE, A. An extended approach to mathematical analysis of programs. (Roughly revised notices to lectures delivered during MFCS-74 Semester in the Intern. Mathem. S.Banach Center in Warsaw, 1974) CC PAS Reports 169(1974)Google Scholar
  5. [5]
    BLIKLE, A. Proving programs by δ-relations. Formalization of Semantics of Programming Languages and Writing of Compilers, (Proc. Symp. Frankfurt/Oder, 1974), Elektronische Informationesverarbeitung und Kybernetik (to appear)Google Scholar
  6. [6]
    BLIKLE, A.; MAZURKIEWICZ, A. An algebraic approach to the theory of programs, algorithms, languages and recursiveness. Math. Found. Comp. Sci. I (Proc. Symp. Warsaw-Jablonna, 1972), Warsaw 1972Google Scholar
  7. [7]
    MANNA, Z.; PNUELI, A. Axiomatic approach to total correctness of programs. Stanford Art. Intel. Lab., Memo AIM-210, Stanford 1973; also Acta Informatica ?(1974)Google Scholar
  8. [8]
    MAZURKIEWICZ, A. Iteratively computable relations. Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 20(1972), 793–798Google Scholar
  9. [9]
    MAZURKIEWICZ, A. Proving properties of processes. CC PAS Reports 134(1973)Google Scholar
  10. [10]
    REDZIEJOWSKI, R.R. The theory of general events and its application to parallel programming. IBM Nordic Laboratory Sweden TP. 18.220 (1972)Google Scholar
  11. [11]
    SCOTT, D. Outline of a mathematical theory of computations. Techn. Mon. PRG-2, Oxford 1970Google Scholar
  12. [12]
    TARSKI, A. A lattice-theoretic fixpoint theorem and its applications. Pacific Jour. Math. 5(1955), 285–309Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • A. Blikle
    • 1
  1. 1.Computation CenterPolish Academy of SciencesWarsawPoland

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