The Construction and Computation of Conditional Statements for SCMPDS

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”.