Abstract
A method of verifying a definite iteration over hierarchical data structures is proposed. 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. Examples which illustrate the application of the method are considered.
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