Volume 8, 1996

University of Bialystok

Copyright (c) 1996 Association of Mizar Users

**Noriko Asamoto**- Ochanomizu University, Tokyo
**Yatsuka Nakamura**- Shinshu University, Nagano
**Piotr Rudnicki**- University of Alberta, Edmonton
**Andrzej Trybulec**- Warsaw University, Bialystok

- This article is a continuation of [15] and [2]. First, we recast the semantics of the macro composition in more convenient terms. Then, we introduce terminology and basic properties of macros constructed out of single instructions of ${\bf SCM}_{\rm FSA}$. We give the complete semantics of composing a macro instruction with an instruction and for composing two machine instructions (this is also done in terms of macros). The introduced terminology is tested on the simple example of a macro for swapping two integer locations.

This work was partially supported by NSERC Grant OGP9207 and NATO CRG 951368.

- Preliminaries
- Parahalting and keeping 0 macro instructions
- Semantics of compositions
- An example: swap

- [1]
Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec.
On the composition of macro instructions. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [2]
Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec.
On the composition of macro instructions. Part III.
*Journal of Formalized Mathematics*, 8, 1996. - [3]
Grzegorz Bancerek.
Cardinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Grzegorz Bancerek and Andrzej Trybulec.
Miscellaneous facts about functions.
*Journal of Formalized Mathematics*, 8, 1996. - [6]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
A classical first order language.
*Journal of Formalized Mathematics*, 2, 1990. - [8]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [9]
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. - [10]
Yatsuka Nakamura and Andrzej Trybulec.
A mathematical model of CPU.
*Journal of Formalized Mathematics*, 4, 1992. - [11]
Piotr Rudnicki and Andrzej Trybulec.
Memory handling for \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [12]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [13]
Andrzej Trybulec and Yatsuka Nakamura.
Some remarks on the simple concrete model of computer.
*Journal of Formalized Mathematics*, 5, 1993. - [14]
Andrzej Trybulec and Yatsuka Nakamura.
Modifying addresses of instructions of \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [15]
Andrzej Trybulec, Yatsuka Nakamura, and Noriko Asamoto.
On the compositions of macro instructions. Part I.
*Journal of Formalized Mathematics*, 8, 1996. - [16]
Andrzej Trybulec, Yatsuka Nakamura, and Piotr Rudnicki.
The \SCMFSA computer.
*Journal of Formalized Mathematics*, 8, 1996. - [17]
Michal J. Trybulec.
Integers.
*Journal of Formalized Mathematics*, 2, 1990. - [18]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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