A THEORY OF PROGRAM EXPANSION
摘要
This paper proposes a theory of program expansion on orthogonal program systems which is a new approach to the analysis, proof and manipulation of computer programs. Its theoretical foundations, expansion methods and applications to programming have been investigated. The existence and uniqueness of program expansions on orthogonal systems have been proved and a condition of convergence obtained. The method of expanding recursire programs is based on the properties of orthogonal mappings. An expansion theorem is proved which can be used to solve both linear and nonlinear recursive equations of program. This paper also gives a number of examples of the application of program expansion to the proof of the properties of programs and to program transformation.