On a symbolic method of verification for definite iteration over data structures

A verification method is proposed for definite iteration over different data structures. The method is based on a replacement operation, which expresses the definite iteration effect in a symbolic form and belongs to a specification language. The method includes a proof rule for the iteration without invariants and inductive proof principles for proving verification conditions which contain the replacement operation. As a case study, a parallel replacement operation for arrays is considered in order to simplify the proof of verification conditions.