Abstract
We present a novel program verification approach based on coinduction, which takes as input an operational semantics. No intermediates like program logics or verification condition generators are needed. Specifications can be written using any state predicates. We implement our approach in Coq, giving a certifying language-independent verification framework. Our proof system is implemented as a single module imported unchanged into language-specific proofs. Automation is reached by instantiating a generic heuristic with language-specific tactics. Manual assistance is also smoothly allowed at points the automation cannot handle. We demonstrate the power and versatility of our approach by verifying algorithms as complicated as Schorr-Waite graph marking and instantiating our framework for object languages in several styles of semantics. Finally, we show that our coinductive approach subsumes reachability logic, a recent language-independent sound and (relatively) complete logic for program verification that has been instantiated with operational semantics of languages as complex as C, Java and JavaScript.
Highlights
Formal verification is a powerful technique for ensuring program correctness, but it requires a suitable verification framework for the target language
Standard approaches such as Hoare logic [1] require significant effort to adapt and prove sound and relatively complete for a given language, with few or no theorems or tools that can be reused between languages
While one can prove Hoare triples valid directly using the step relation →R and induction, or coinduction like we propose in this paper, the traditional approach is to define a language-specific proof system for deriving Hoare triples from other triples, known as a Hoare logic, or program logic, for the target programming language
Summary
Formal verification is a powerful technique for ensuring program correctness, but it requires a suitable verification framework for the target language. Standard approaches such as Hoare logic [1] (or verification condition generators) require significant effort to adapt and prove sound and relatively complete for a given language, with few or no theorems or tools that can be reused between languages. To use a software engineering metaphor, Hoare logic is a design pattern rather than a library. This becomes literal when we formalize it in a proof assistant. The core of our approach is a simple theorem which gives a coinduction principle for proving partial correctness
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