Volume 11, 1999

University of Bialystok

Copyright (c) 1999 Association of Mizar Users

**Jing-Chao Chen**- Shanghai Jiaotong University

- In this article, a program block is defined as a finite sequence of instructions stored consecutively on initial positions. Based on this definition,any program block with more than two instructions can be viewed as the combination of two smaller program blocks. To describe the computation of a program block by the result of its two sub-blocks, we introduce the notions of paraclosed, parahalting, valid, and shiftable, the meaning of which may be stated as follows: \begin{itemize} \item[-] a program is paraclosed if and only if any state containing it is closed, \item[-] a program is parahalting if and only if any state containing it is halting, \item[-] in a program block, a jumping instruction is valid if its jumping offset is valid, \item[-] a program block is shiftable if it does not contain any return and saveIC instructions, and each instruction in it is valid. \end{itemize} When a program block is shiftable, its computing result does not depend on its storage position.

This research is partially supported by the National Natural Science Foundation of China Grant No. 69873033.

- Definition of a Program Block and its Basic Properties
- Combining two Consecutive Blocks into One Program Block
- Combining a Block and a Instruction into One Program Block
- The Notions of Paraclosed, Parahalting and their Basic Properties
- Shiftability of Program Blocks and Instructions

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