Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

## Two Programs for \bf SCM. Part I - Preliminaries

Grzegorz Bancerek
Polish Academy of Sciences, Institute of Mathematics, Warsaw
Piotr Rudnicki
University of Alberta, Department of Computing Science, Edmonton

### Summary.

In two articles (this one and [4]) we discuss correctness of two short programs for the {\bf SCM} machine: one computes Fibonacci numbers and the other computes the {\em fusc} function of Dijkstra [9]. The limitations of current Mizar implementation rendered it impossible to present the correctness proofs for the programs in one article. This part is purely technical and contains a number of very specific lemmas about integer division, floor, exponentiation and logarithms. The formal definitions of the Fibonacci sequence and the {\em fusc} function may be of general interest.

This work was partially supported by NSERC Grant OGP9207 while the first author visited University of Alberta, May--June 1993.

#### MML Identifier: PRE_FF

The terminology and notation used in this paper have been introduced in the following articles [7] [16] [2] [13] [14] [1] [12] [11] [10] [5] [6] [3] [8] [15]

Contents (PDF format)

#### Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek and Piotr Rudnicki. Two programs for \bf scm. Part II - programs. Journal of Formalized Mathematics, 5, 1993.
[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[9] Edsger W. Dijkstra. \em Selected Writings on Computing, a Personal Perspective.
[10] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms. Journal of Formalized Mathematics, 2, 1990.
[11] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[12] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[13] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[14] Michal J. Trybulec. Integers. Journal of Formalized Mathematics, 2, 1990.
[15] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[16] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.