1,004 research outputs found
First steps towards the certification of an ARM simulator using Compcert
The simulation of Systems-on-Chip (SoC) is nowadays a hot topic because,
beyond providing many debugging facilities, it allows the development of
dedicated software before the hardware is available. Low-consumption CPUs such
as ARM play a central role in SoC. However, the effectiveness of simulation
depends on the faithfulness of the simulator. To this effect, we propose here
to prove significant parts of such a simulator, SimSoC. Basically, on one hand,
we develop a Coq formal model of the ARM architecture while on the other hand,
we consider a version of the simulator including components written in
Compcert-C. Then we prove that the simulation of ARM operations, according to
Compcert-C formal semantics, conforms to the expected formal model of ARM. Size
issues are partly dealt with using automatic generation of significant parts of
the Coq model and of SimSoC from the official textual definition of ARM.
However, this is still a long-term project. We report here the current stage of
our efforts and discuss in particular the use of Compcert-C in this framework.Comment: First International Conference on Certified Programs and Proofs 7086
(2011
CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates
Termination is an important property of programs; notably required for
programs formulated in proof assistants. It is a very active subject of
research in the Turing-complete formalism of term rewriting systems, where many
methods and tools have been developed over the years to address this problem.
Ensuring reliability of those tools is therefore an important issue. In this
paper we present a library formalizing important results of the theory of
well-founded (rewrite) relations in the proof assistant Coq. We also present
its application to the automated verification of termination certificates, as
produced by termination tools
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
Perspectives for proof unwinding by programming languages techniques
In this chapter, we propose some future directions of work, potentially
beneficial to Mathematics and its foundations, based on the recent import of
methodology from the theory of programming languages into proof theory. This
scientific essay, written for the audience of proof theorists as well as the
working mathematician, is not a survey of the field, but rather a personal view
of the author who hopes that it may inspire future and fellow researchers
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
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