Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

On the Composition of Macro Instructions. Part III


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

Summary.

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.

MML Identifier: SCMFSA6C

The terminology and notation used in this paper have been introduced in the following articles [12] [17] [18] [6] [4] [8] [3] [7] [9] [10] [13] [5] [16] [14] [15] [11] [1]

Contents (PDF format)

  1. Preliminaries
  2. Parahalting and keeping 0 macro instructions
  3. Semantics of compositions
  4. An example: swap

Bibliography

[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.

Received July 22, 1996


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