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

Bounded Refinement Types

We present a notion of bounded quantification for refinement types and show how it expands the expressiveness of refinement typing by using it to develop typed combinators for: (1) relational algebra and safe database access, (2) Floyd-Hoare logic within a state transformer monad equipped with combinators for branching and looping, and (3) using the above to implement a refined IO monad that tracks capabilities and resource usage. This leap in expressiveness comes via a translation to "ghost" functions, which lets us retain the automated and decidable SMT based checking and inference that makes refinement typing effective in practice.Comment: 14 pages, International Conference on Functional Programming, ICFP 201

A Graphical User Interface for Formal Proofs in Geometry.

International audienceWe present in this paper the design of a graphical user interface to deal with proofs in geometry. The software developed combines three tools: a dynamic geometry software to explore, measure and invent conjectures, an automatic theorem prover to check facts and an interactive proof system (Coq) to mechanically check proofs built interactively by the user

SEPIA: Search for Proofs Using Inferred Automata

This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show that SEPIA provides a useful complement to existing automated tactics in Coq.Comment: To appear at 25th International Conference on Automated Deductio

Formal Proof of SCHUR Conjugate Function

The main goal of our work is to formally prove the correctness of the key commands of the SCHUR software, an interactive program for calculating with characters of Lie groups and symmetric functions. The core of the computations relies on enumeration and manipulation of combinatorial structures. As a first "proof of concept", we present a formal proof of the conjugate function, written in C. This function computes the conjugate of an integer partition. To formally prove this program, we use the Frama-C software. It allows us to annotate C functions and to generate proof obligations, which are proved using several automated theorem provers. In this paper, we also draw on methodology, discussing on how to formally prove this kind of program.Comment: To appear in CALCULEMUS 201

"5 Days in August" – How London Local Authorities used Twitter during the 2011 riots

© IFIP International Federation for Information Processing 2012This study examines effects of microblogging communications during emergency events based on the case of the summer 2011 riots in London. During five days in August 2011, parts of London and other major cities in England suffered from extensive public disorders, violence and even loss of human lives. We collected and analysed the tweets posted by the official accounts maintained by 28 London local government authorities. Those authorities used Twitter for a variety of purposes such as preventing rumours, providing official information, promoting legal actions against offenders and organising post-riot community engagement activities. The study shows how the immediacy and communicative power of microblogging can have a significant effect at the response and recovery stages of emergency events

Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more than a decade of CPU time and produced 27 GB of proof witnesses. The checker uses an untrusted oracle based on these witnesses and is able to verify the smaller case of 8 inputs within a couple of days, but it did not scale to the full proof for 9 inputs. In this paper, we describe several non-trivial optimizations of the algorithm in the checker, obtained by appropriately changing the formalization and capitalizing on the symbiosis with an adequate implementation of the oracle. We provide experimental evidence of orders of magnitude improvements to both runtime and memory footprint for 8 inputs, and actually manage to check the full proof for 9 inputs.Comment: IMADA-preprint-c

Towards Generic Monitors for Object-Oriented Real-Time Maude Specifications

Non-Functional Properties (NFPs) are crucial in the design of software. Specification of systems is used in the very first phases of the software development process for the stakeholders to make decisions on which architecture or platform to use. These specifications may be an- alyzed using different formalisms and techniques, simulation being one of them. During a simulation, the relevant data involved in the anal- ysis of the NFPs of interest can be measured using monitors. In this work, we show how monitors can be parametrically specified so that the instrumentation of specifications to be monitored can be automatically performed. We prove that the original specification and the automati- cally obtained specification with monitors are bisimilar by construction. This means that the changes made on the original system by adding monitors do not affect its behavior. This approach allows us to have a library of possible monitors that can be safely added to analyze different properties, possibly on different objects of our systems, at will.Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech. Spanish MINECO/FEDER project TIN2014-52034-R, NSF Grant CNS 13-19109

Automatically proving equivalence by type-safe reflection

We are also grateful for the support of the Scottish Informatics and Computer Science Alliance (SICSA) and EPSRC grant EP/N024222/1.One difficulty with reasoning and programming with dependent types is that proof obligations arise naturally once programs become even moderately sized. For example, implementing an adder for binary numbers indexed over their natural number equivalents naturally leads to proof obligations for equalities of expressions over natural numbers. The need for these equality proofs comes, in intensional type theories, from the fact that the propositional equality enables us to prove as equal terms that are not judgementally equal, which means that the typechecker can’t always obtain equalities by reduction. As far as possible, we would like to solve such proof obligations automatically. In this paper, we show one way to automate these proofs by reflection in the dependently typed programming language Idris. We show how defining reflected terms indexed by the original Idris expression allows us to construct and manipulate proofs. We build a hierarchy of tactics for proving equivalences in semi-groups, monoids, commutative monoids, groups, commutative groups, semi-rings and rings. We also show how each tactic reuses those from simpler structures, thus avoiding duplication of code and proofs.Postprin