Volume 10, 1998

University of Bialystok

Copyright (c) 1998 Association of Mizar Users

**Piotr Rudnicki**- University of Alberta, Edmonton
- This work was partially supported by NSERC Grant OGP9207 and NATO CRG 951368.

- An attempt to use the {\tt while} macro, [16], was the origin of writing this article. The {\tt while} semantics, as given by J.-C.~Chen, is slightly extended by weakening its correctness conditions and this forced a quite straightforward remake of a number of theorems from [16]. Numerous additional properties of the {\tt while} macro are then proven. In the last section, we define a macro instruction computing the {\tt fusc} function (see the SCM program computing the same function in [12]) and prove its correctness.

- Arithmetic Preliminaries
- {\SCMFSA} Preliminaries
- The {\tt while=0} Macro Instruction
- The {\tt while>0} Macro Instruction
- A Macro for the {\tt fusc} Function

- [1]
Noriko Asamoto.
Conditional branch macro instructions of \SCMFSA. Part I.
*Journal of Formalized Mathematics*, 8, 1996. - [2]
Noriko Asamoto.
Conditional branch macro instructions of \SCMFSA. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [3]
Noriko Asamoto.
Constant assignment macro instructions of \SCMFSA. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [4]
Noriko Asamoto.
Some multi instructions defined by sequence of instructions of \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [5]
Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec.
On the composition of macro instructions. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [6]
Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec.
On the composition of macro instructions. Part III.
*Journal of Formalized Mathematics*, 8, 1996. - [7]
Grzegorz Bancerek.
Cardinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Grzegorz Bancerek.
K\"onig's theorem.
*Journal of Formalized Mathematics*, 2, 1990. - [10]
Grzegorz Bancerek and Piotr Rudnicki.
Development of terminology for \bf scm.
*Journal of Formalized Mathematics*, 5, 1993. - [11]
Grzegorz Bancerek and Piotr Rudnicki.
Two programs for \bf scm. Part I - preliminaries.
*Journal of Formalized Mathematics*, 5, 1993. - [12]
Grzegorz Bancerek and Piotr Rudnicki.
Two programs for \bf scm. Part II - programs.
*Journal of Formalized Mathematics*, 5, 1993. - [13]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
*Journal of Formalized Mathematics*, 2, 1990. - [16]
Jing-Chao Chen.
While macro instructions of \SCMFSA.
*Journal of Formalized Mathematics*, 9, 1997. - [17]
Yatsuka Nakamura and Andrzej Trybulec.
A mathematical model of CPU.
*Journal of Formalized Mathematics*, 4, 1992. - [18]
Piotr Rudnicki.
On the composition of non-parahalting macro instructions.
*Journal of Formalized Mathematics*, 10, 1998. - [19]
Piotr Rudnicki and Andrzej Trybulec.
Memory handling for \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [20]
Piotr Rudnicki and Andrzej Trybulec.
Abian's fixed point theorem.
*Journal of Formalized Mathematics*, 9, 1997. - [21]
Yasushi Tanaka.
On the decomposition of the states of SCM.
*Journal of Formalized Mathematics*, 5, 1993. - [22]
Andrzej Trybulec.
Binary operations applied to functions.
*Journal of Formalized Mathematics*, 1, 1989. - [23]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [24]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [25]
Andrzej Trybulec and Agata Darmochwal.
Boolean domains.
*Journal of Formalized Mathematics*, 1, 1989. - [26]
Andrzej Trybulec and Yatsuka Nakamura.
Some remarks on the simple concrete model of computer.
*Journal of Formalized Mathematics*, 5, 1993. - [27]
Andrzej Trybulec and Yatsuka Nakamura.
Modifying addresses of instructions of \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [28]
Andrzej Trybulec, Yatsuka Nakamura, and Noriko Asamoto.
On the compositions of macro instructions. Part I.
*Journal of Formalized Mathematics*, 8, 1996. - [29]
Andrzej Trybulec, Yatsuka Nakamura, and Piotr Rudnicki.
The \SCMFSA computer.
*Journal of Formalized Mathematics*, 8, 1996. - [30]
Michal J. Trybulec.
Integers.
*Journal of Formalized Mathematics*, 2, 1990. - [31]
Wojciech A. Trybulec.
Groups.
*Journal of Formalized Mathematics*, 2, 1990. - [32]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [33]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

[ Download a postscript version, MML identifier index, Mizar home page]