Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

Another \tt times Macro Instruction

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

Summary.

The semantics of the {\tt times} macro is given in [2] only for the case when the body of the macro is parahalting. We remedy this by defining a new {\tt times} macro instruction in terms of {\tt while} (see [11], [14]). The semantics of the new {\tt times} macro is given in a way analogous to the semantics of {\tt while} macros. The new {\tt times} uses an anonymous variable to control the number of its executions. We present two examples: a trivial one and a remake of the macro for the Fibonacci sequence (see [13]).

MML Identifier: SFMASTR2

The terminology and notation used in this paper have been introduced in the following articles [16] [21] [17] [6] [5] [22] [8] [9] [10] [7] [12] [18] [20] [19] [3] [15] [4] [1] [11] [13]

Contents (PDF format)

1. {\SCMFSA} Preliminaries
2. Another {\tt times} Macro Instruction
3. A Trivial Example
4. A Macro for the Fibonacci Sequence

Bibliography

[1] Noriko Asamoto. Constant assignment macro instructions of \SCMFSA. Part II. Journal of Formalized Mathematics, 8, 1996.
[2] Noriko Asamoto. The \tt loop and \tt times macroinstruction for \SCMFSA. Journal of Formalized Mathematics, 9, 1997.
[3] Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec. On the composition of macro instructions. Part II. Journal of Formalized Mathematics, 8, 1996.
[4] Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec. On the composition of macro instructions. Part III. Journal of Formalized Mathematics, 8, 1996.
[5] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[6] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[7] Grzegorz Bancerek and Piotr Rudnicki. Two programs for \bf scm. Part I - preliminaries. Journal of Formalized Mathematics, 5, 1993.
[8] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[10] 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.
[11] Jing-Chao Chen. While macro instructions of \SCMFSA. Journal of Formalized Mathematics, 9, 1997.
[12] Yatsuka Nakamura and Andrzej Trybulec. A mathematical model of CPU. Journal of Formalized Mathematics, 4, 1992.
[13] Piotr Rudnicki. On the composition of non-parahalting macro instructions. Journal of Formalized Mathematics, 10, 1998.
[14] Piotr Rudnicki. The \tt while macro instructions of \SCMFSA. Part II. Journal of Formalized Mathematics, 10, 1998.
[15] Piotr Rudnicki and Andrzej Trybulec. Memory handling for \SCMFSA. Journal of Formalized Mathematics, 8, 1996.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[17] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[18] Andrzej Trybulec and Yatsuka Nakamura. Some remarks on the simple concrete model of computer. Journal of Formalized Mathematics, 5, 1993.
[19] Andrzej Trybulec, Yatsuka Nakamura, and Noriko Asamoto. On the compositions of macro instructions. Part I. Journal of Formalized Mathematics, 8, 1996.
[20] Andrzej Trybulec, Yatsuka Nakamura, and Piotr Rudnicki. The \SCMFSA computer. Journal of Formalized Mathematics, 8, 1996.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.