Volume 11, 1999

University of Bialystok

Copyright (c) 1999 Association of Mizar Users

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

- We construct conditional statements like the usual high level program language by program blocks of SCMPDS. Roughly speaking, the article justifies such a fact that when the condition of a conditional statement is true (false), and the true (false) branch is shiftable, parahalting and does not contain any halting instruction, and the false branch is shiftable, then it is halting and its computation result equals that of the true (false) branch. The parahalting means some program halts for all states, this is strong condition. For this reason, we introduce the notions of "is\_closed\_on" and "is\_halting\_on". The predicate "A is\_closed\_on B" denotes program A is closed on state B, and "A is\_halting\_on B" denotes program A is halting on state B. We obtain a similar theorem to the above fact by replacing parahalting by "is\_closed\_on" and "is\_halting\_on".

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

- Preliminaries
- The Predicates of is\_closed\_on and is\_halting\_on
- The Construction of Conditional Statements
- The Computation of ``if var=0 then block1 else block2''
- The Computation of ``if var=0 then block''
- The Computation of ``if var<>0 then block''
- The Computation of ``if var>0 then block1 else block2''
- The Computation of ``if var>0 then block''
- The Computation of ``if var<=0 then block''
- The Computation of ``if var<0 then block1 else block2''
- The Computation of ``if var<0 then block''
- The Computation of ``if var>=0 then block''

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