Integrating different versions of programs with backward and forward slices

A program difference integration algorithm, which integrates two different versions of programs derived from an original program into a common one, is given. The algorithm uses two kinds of program slices: backward slice and forward slice, which enables the algorithm to integrate a class of programs that cannot be integrated by the existing algorithms. The class includes such significant programs that one version is obtained by modifying then clause of an if statement in the original program and the other is obtained by modifying else clause of the if statement. It is also shown that the algorithm satisfies associativity by regarding a program as a Boolean algebra in which the algorithm is expressed by an integration operation whose associativity is easily proved. The algorithmʹs associativity is shown by the correspondence between the algorithm and the algebra.