This paper introduces a methodology to perform formal verification of floating-point C programs. It extends an existing tool for the verification of C programs, Caduceus, with new annotations specific to floating-point arithmetic. The Caduceus first-order logic model for C programs is extended accordingly. Then verification conditions expressing the correctness of the programs are obtained in the usual way and can be discharged interactively with the Coq proof assistant, using an existing Coq formalization of floatingpoint arithmetic. This methodology is already implemented and has been successfully applied to several short floatingpoint programs, which are presented in this paper.
This paper introduces GOSPEL, a behavioral specification language for OCaml. It is designed to enable modular verification of data structures and algorithms. GOSPEL is a contract-based, strongly typed language, with a formal semantics defined by means of translation into Separation Logic. Compared with writing specifications directly in Separation Logic, GOSPEL provides a high-level syntax that greatly improves conciseness and makes it accessible to programmers with no familiarity with Separation Logic. Although GOSPEL has been developed for specifying OCaml code, we believe that many aspects of its design could apply to other programming languages. This paper presents the design and semantics of GOSPEL, and reports on its application for the development of a formally verified library of general-purpose OCaml data structures.
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