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Procedures, formal computations and models

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

Abstract

Starting from the logical point of view we conceive procedures as formulas of a formalized algorithmic language defining functions and/or relations. The notion of formal computation is introduced in a way resembling formal proofs. Computations may serve to extend the original interpretation of the language onto symbols defined by procedures. The main result is: if a system of procedures is consistent then the computed extension of a given interpretation is the smallest model of the system. From this the principle of recursion induction can be proved. A technique transforming any system of procedures to a consistent system of conditional recursive definitions is shown.

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References

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    Dańko, W. Not programmable function defined by a procedure. Bull.Acad.Pol.Sci. Ser.Math.Astr.Phys. 22 1974 587–594Google Scholar
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    Mirkowska, G. On formalized systems of algorithmic logic. ibid. 21 1971 421–428Google Scholar
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    Rasiowa, H.; Sikorski, R. Mathematics of metamathematics. PWN, Warszawa 1963Google Scholar
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    Salwicki, A. Formalized algorithmic languages. Bull.acd, Pol. Sci. Ser.Math.Astr.Phys. 18 1970 227–232Google Scholar
  5. [5]
    Salwicki,A. Programmability and recursiveness, an application of algorithmic logic to procedures. to appear in Dissert.Math.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Andrzej Salwicki
    • 1
  1. 1.Institute of Mathematical MachinesWarsaw UniversityWarszawa PKiN VIIIpPoland

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