Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program

Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring specific accuracy issues due to their massive use of floating-point computations. Yet, it is uncommon to guarantee their correctness. Indeed, we had to extend existing methods and tools for proving the correct behavior of programs to verify an existing numerical analysis program. This C program implements the second-order centered finite difference explicit scheme for solving the 1D wave equation. In fact, we have gone much further as we have mechanically verified the convergence of the numerical scheme in order to get a complete formal proof covering all aspects from partial differential equations to actual numerical results. To the best of our knowledge, this is the first time such a comprehensive proof is achieved.Comment: N° RR-8197 (2012). arXiv admin note: text overlap with arXiv:1112.179

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

Deductive Verification of Parallel Programs Using Why3

The Message Passing Interface specification (MPI) defines a portable message-passing API used to program parallel computers. MPI programs manifest a number of challenges on what concerns correctness: sent and expected values in communications may not match, resulting in incorrect computations possibly leading to crashes; and programs may deadlock resulting in wasted resources. Existing tools are not completely satisfactory: model-checking does not scale with the number of processes; testing techniques wastes resources and are highly dependent on the quality of the test set. As an alternative, we present a prototype for a type-based approach to programming and verifying MPI like programs against protocols. Protocols are written in a dependent type language designed so as to capture the most common primitives in MPI, incorporating, in addition, a form of primitive recursion and collective choice. Protocols are then translated into Why3, a deductive software verification tool. Source code, in turn, is written in WhyML, the language of the Why3 platform, and checked against the protocol. Programs that pass verification are guaranteed to be communication safe and free from deadlocks. We verified several parallel programs from textbooks using our approach, and report on the outcome.Comment: In Proceedings ICE 2015, arXiv:1508.0459

Mechanizing a Process Algebra for Network Protocols

This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in Isabelle/HOL is relatively standard, but its layered structure necessitates special treatment. The control states of reactive processes, such as nodes in a network, are modelled by terms of the process algebra. We propose a technique based on these terms to streamline proofs of inductive invariance. This is not sufficient, however, to state and prove invariants that relate states across multiple processes (entire networks). To this end, we propose a novel compositional technique for lifting global invariants stated at the level of individual nodes to networks of nodes.Comment: This paper is an extended version of arXiv:1407.3519. The Isabelle/HOL source files, and a full proof document, are available in the Archive of Formal Proofs, at http://afp.sourceforge.net/entries/AWN.shtm

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin