Formalizing Single-Assignment Program Verification: An Adaptation-Complete Approach

Deductive verification tools typically rely on the conversion of code to a single-assignment (SA) form. In this paper we formalize program verification based on the translation of While programs annotated with loop invariants into a dynamic single-assignment language with a dedicated iterating construct, and the subsequent generation of compact, indeed linear-size, verification conditions. Soundness and completeness proofs are given for the entire workflow, including the translation of annotated programs to SA form. The formalization is based on a program logic that we show to be adaptation-complete. Although this important property has not, as far as we know, been established for any existing program verification tool, we believe that adaptation-completeness is one of the major motivations for the use of SA form as an intermediate language. Our results here show that indeed this allows for the tools to achieve the maximum degree of adaptation when handling subprograms.- This work is financed by the ERDF-European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme, and by National Funds through the FCT-Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) within project "POCI-01-0145-FEDER-006961". The first author is also sponsored by FCT grant SFRH/BD/52236/2013.