Reasoning about Iteration and Recursion Uniformly based on Big-step Semantics (2108.01883v1)

Abstract: A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious undertaking. In language-independent program verification, common aspects of computer programs are addressed to enable sound reasoning for all languages. In this work, we propose a solution for the sound reasoning about iteration and recursion based on the big-step operational semantics of any programming language. We give inductive proofs on the soundness and relative completeness of our reasoning technique. We illustrate the technique at simplified programming languages of the imperative and functional paradigms, with diverse features. We also mechanism all formal results in the Coq proof assistant.