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
Dańko, W. Not programmable function defined by a procedure. Bull.Acad.Pol.Sci. Ser.Math.Astr.Phys. 22 1974 587–594
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Salwicki, A. Formalized algorithmic languages. Bull.acd, Pol. Sci. Ser.Math.Astr.Phys. 18 1970 227–232
Salwicki,A. Programmability and recursiveness, an application of algorithmic logic to procedures. to appear in Dissert.Math.
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© 1975 Springer-Verlag Berlin Heidelberg
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Salwicki, A. (1975). Procedures, formal computations and models. In: Blikle, A. (eds) Mathematical Foundations of Computer Science. MFCS 1974. Lecture Notes in Computer Science, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07162-8_704
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DOI: https://doi.org/10.1007/3-540-07162-8_704
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