Section: New Results

Certification of Languages, Tools and Systems

• M. Clochard and L. Gondelman developed a formalization of a simple compiler in Why3. It compiles a simple imperative language into assembler instructions for a stack machine. This case study was inspired by a similar example developed using Coq and interactive theorem proving. The aim is to improve significantly the degree of automation in the proofs. This is achieved by the formalization of a Hoare logic and a Weakest Precondition Calculus on assembly programs, so that the correctness of compilation is seen as a formal specification of the assembly instructions generated. This work was presented at the JFLA conference in 2015 [25] .

• S. Boldo, C. Lelay, and G. Melquiond worked on the Coquelicot library, designed to be a user-friendly Coq library about real analysis. An easier way of writing formulas and theorem statements is achieved by relying on total functions in place of dependent types for limits, derivatives, integrals, power series, and so on. To help with the proof process, the library comes with a comprehensive set of theorems and some automation. We have exercised the library on several use cases: in an exam at university entry level, for the definitions and properties of Bessel functions, and for the solution of the one-dimensional wave equation. These results are published in the journal Mathematics in Computer Science [14] .

• C. Lelay developed a new formalization of convergence with a focus on usability and genericity for the Coquelicot library. This formalization covers various parts of analysis: sequences, real functions, complex functions, vector functions, and so on. This work was presented at the 7th Coq Workshop [27] .

• C. Paulin wrote a gentle introduction to the Calculus of Inductive Construction, the formalism on which the Coq proof assistant is based [28] , discussing both theoretical and pragmatic aspects of the design.