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

On relating CTL to Datalog

CTL is the dominant temporal specification language in practice mainly due to the fact that it admits model checking in linear time. Logic programming and the database query language Datalog are often used as an implementation platform for logic languages. In this paper we present the exact relation between CTL and Datalog and moreover we build on this relation and known efficient algorithms for CTL to obtain efficient algorithms for fragments of stratified Datalog. The contributions of this paper are: a) We embed CTL into STD which is a proper fragment of stratified Datalog. Moreover we show that STD expresses exactly CTL -- we prove that by embedding STD into CTL. Both embeddings are linear. b) CTL can also be embedded to fragments of Datalog without negation. We define a fragment of Datalog with the successor build-in predicate that we call TDS and we embed CTL into TDS in linear time. We build on the above relations to answer open problems of stratified Datalog. We prove that query evaluation is linear and that containment and satisfiability problems are both decidable. The results presented in this paper are the first for fragments of stratified Datalog that are more general than those containing only unary EDBs.Comment: 34 pages, 1 figure (file .eps

Model-driven Information Flow Security for Component-Based Systems

International audienceThis paper proposes a formal framework for studying information flow security in component-based systems. The security policy is defined and verified from the early steps of the system design. Two kinds of non-interference properties are formally introduced and for both of them, sufficient conditions that ensures and simplifies the automated verification are proposed. The verification is compositional, first locally, by checking the behavior of every atomic component and then globally, by checking the inter-components communication and coordination. The potential benefits are illustrated on a concrete case study about constructing secure heterogeneous distributed systems

Feasible Computation in Symbolic and Numeric Integration

Two central concerns in scientific computing are the reliability and efficiency of algorithms. We introduce the term feasible computation to describe algorithms that are reliable and efficient given the contextual constraints imposed in practice. The main focus of this dissertation then, is to bring greater clarity to the forms of error introduced in computation and modeling, and in the limited context of symbolic and numeric integration, to contribute to integration algorithms that better account for error while providing results efficiently. Chapter 2 considers the problem of spurious discontinuities in the symbolic integration problem, proposing a new method to restore continuity based on a pair of unwinding numbers. Computable conditions for the unwinding numbers are specified, allowing the computation of a variety of continuous integrals. Chapter 3 introduces two structure-preserving algorithms for the symbolic-numeric integration of rational functions on exact input. A structured backward and forward error analysis for the algorithms shows that they are a posteriori backward and forward stable, with both forms of error exhibiting tolerance proportionality. Chapter 4 identifies the basic logical structure of feasible inference by presenting a logical model of stable approximate inference, illustrated by examples of modeling and numerical integration. In terms of this model it is seen that a necessary condition for the feasibility of methods of abstraction in modeling and complexity reduction in computational mathematics is the preservation of inferential structure, in a sense that is made precise. Chapter 5 identifies a robust pattern in mathematical sciences of transforming problems to make solutions feasible. It is showed that computational complexity reduction methods in computational science involve chains of such transformations. It is argued that the structured and approximate nature of such strategies indicates the need for a higher-order model of computation and a new definition of computational complexity

Micro Virtual Machines: A Solid Foundation for Managed Language Implementation

Today new programming languages proliferate, but many of them suffer from poor performance and inscrutable semantics. We assert that the root of many of the performance and semantic problems of today's languages is that language implementation is extremely difficult. This thesis addresses the fundamental challenges of efficiently developing high-level managed languages. Modern high-level languages provide abstractions over execution, memory management and concurrency. It requires enormous intellectual capability and engineering effort to properly manage these concerns. Lacking such resources, developers usually choose naive implementation approaches in the early stages of language design, a strategy which too often has long-term consequences, hindering the future development of the language. Existing language development platforms have failed to provide the right level of abstraction, and forced implementers to reinvent low-level mechanisms in order to obtain performance. My thesis is that the introduction of micro virtual machines will allow the development of higher-quality, high-performance managed languages. The first contribution of this thesis is the design of Mu, with the specification of Mu as the main outcome. Mu is the first micro virtual machine, a robust, performant, and light-weight abstraction over just three concerns: execution, concurrency and garbage collection. Such a foundation attacks three of the most fundamental and challenging issues that face existing language designs and implementations, leaving the language implementers free to focus on the higher levels of their language design. The second contribution is an in-depth analysis of on-stack replacement and its efficient implementation. This low-level mechanism underpins run-time feedback-directed optimisation, which is key to the efficient implementation of dynamic languages. The third contribution is demonstrating the viability of Mu through RPython, a real-world non-trivial language implementation. We also did some preliminary research of GHC as a Mu client. We have created the Mu specification and its reference implementation, both of which are open-source. We show that that Mu's on-stack replacement API can gracefully support dynamic languages such as JavaScript, and it is implementable on concrete hardware. Our RPython client has been able to translate and execute non-trivial RPython programs, and can run the RPySOM interpreter and the core of the PyPy interpreter. With micro virtual machines providing a low-level substrate, language developers now have the option to build their next language on a micro virtual machine. We believe that the quality of programming languages will be improved as a result

Unwinding biological systems

Unwinding conditions have been fruitfully exploited in Information Flow Security to define persistent security properties. In this paper we investigate their meaning and possible uses in the analysis of biological systems. In particular, we elaborate on the notion of robustness and propose some instances of unwinding over the process algebra Bio-PEPA and over hybrid automata. We exploit such instances to analyse two case-studies: Neurospora crassa circadian system and Influenza kinetics models