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 Times} macro, [2], was the origin of writing this article. First, the semantics of the macro composition as developed in [26], [3], [4] is extended to the case of macro instructions which are not always halting. Next, several functors extending the memory handling for {\SCMFSA}, [19], are defined; they are convenient when writing more complicated programs. After this preparatory work, we define a macro instruction computing the Fibonacci sequence (see the SCM program computing the same sequence in [9]) and prove its correctness. The semantics of the {\tt Times} macro is given in [2] only for the case when the iterated instruction is parahalting; this is remedied in [18].

- Good Instructions and Good Macro Instruction
- Composition of Non-parahalting Macro Instructions
- Memory Allocation
- A Macro for the Fibonacci Sequence

- [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.
Cardinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Grzegorz Bancerek and Piotr Rudnicki.
Development of terminology for \bf scm.
*Journal of Formalized Mathematics*, 5, 1993. - [8]
Grzegorz Bancerek and Piotr Rudnicki.
Two programs for \bf scm. Part I - preliminaries.
*Journal of Formalized Mathematics*, 5, 1993. - [9]
Grzegorz Bancerek and Piotr Rudnicki.
Two programs for \bf scm. Part II - programs.
*Journal of Formalized Mathematics*, 5, 1993. - [10]
Grzegorz Bancerek and Andrzej Trybulec.
Miscellaneous facts about functions.
*Journal of Formalized Mathematics*, 8, 1996. - [11]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [12]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
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. - [15]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [16]
Agata Darmochwal and Andrzej Trybulec.
Similarity of formulae.
*Journal of Formalized Mathematics*, 3, 1991. - [17]
Yatsuka Nakamura and Andrzej Trybulec.
A mathematical model of CPU.
*Journal of Formalized Mathematics*, 4, 1992. - [18]
Piotr Rudnicki.
Another \tt times macro instruction.
*Journal of Formalized Mathematics*, 10, 1998. - [19]
Piotr Rudnicki and Andrzej Trybulec.
Memory handling for \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [20]
Yasushi Tanaka.
On the decomposition of the states of SCM.
*Journal of Formalized Mathematics*, 5, 1993. - [21]
Andrzej Trybulec.
Enumerated sets.
*Journal of Formalized Mathematics*, 1, 1989. - [22]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [23]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [24]
Andrzej Trybulec and Yatsuka Nakamura.
Some remarks on the simple concrete model of computer.
*Journal of Formalized Mathematics*, 5, 1993. - [25]
Andrzej Trybulec and Yatsuka Nakamura.
Modifying addresses of instructions of \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [26]
Andrzej Trybulec, Yatsuka Nakamura, and Noriko Asamoto.
On the compositions of macro instructions. Part I.
*Journal of Formalized Mathematics*, 8, 1996. - [27]
Andrzej Trybulec, Yatsuka Nakamura, and Piotr Rudnicki.
The \SCMFSA computer.
*Journal of Formalized Mathematics*, 8, 1996. - [28]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [29]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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