A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems

Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the issues of defining such sequent calculi for Pure Type Systems (PTS, which were originally presented in natural deduction style) and then organizing their rules for effective proof-search. We introduce the idea of Pure Type Sequent Calculus with meta-variables (PTSCalpha), by enriching the syntax of a permutation-free sequent calculus for propositional logic due to Herbelin, which is strongly related to natural deduction and already well adapted to proof-search. The operational semantics is adapted from Herbelin's and is defined by a system of local rewrite rules as in cut-elimination, using explicit substitutions. We prove confluence for this system. Restricting our attention to PTSC, a type system for the ground terms of this system, we obtain the Subject Reduction property and show that each PTSC is logically equivalent to its corresponding PTS, and the former is strongly normalising iff the latter is. We show how to make the logical rules of PTSC into a syntax-directed system PS for proof-search, by incorporating the conversion rules as in syntax-directed presentations of the PTS rules for type-checking. Finally, we consider how to use the explicitly scoped meta-variables of PTSCalpha to represent partial proof-terms, and use them to analyse interactive proof construction. This sets up a framework PE in which we are able to study proof-search strategies, type inhabitant enumeration and (higher-order) unification

Characterising strongly normalising intuitionistic sequent terms

This paper gives a characterisation, via intersection types, of the strongly normalising terms of an intuitionistic sequent calculus (where LJ easily embeds). The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary lambda-calculus. The completeness of the typing system is obtained from subject expansion at root position. This paper's sequent term calculus integrates smoothly the lambda-terms with generalised application or explicit substitution. Strong normalisability of these terms as sequent terms characterises their typeability in certain "natural'' typing systems with intersection types. The latter are in the natural deduction format, like systems previously studied by Matthes and Lengrand et al., except that they do not contain any extra, exceptional rules for typing generalised applications or substitution

Focalisation and Classical Realisability (version with appendices)

The original publication is avalaible at : www.springerlink.comInternational audienceWe develop a polarised variant of Curien and Herbelin's lambda-bar-mu-mu-tilde calculus suitable for sequent calculi that admit a focalising cut elimination (i.e. whose proofs are focalised when cut-free), such as Girard's classical logic LC or linear logic. This gives a setting in which Krivine's classical realisability extends naturally (in particular to call-by-value), with a presentation in terms of orthogonality. We give examples of applications to the theory of programming languages

Innovation Management Techniques and Tools: a review from Theory and Practice

Knowledge is considered to be an economic driver in today’s economy. It has become a commodity, a resource that can be packed and transferred. The objective of this paper is to provide a comprehensive review of the scope, trends and major actors (firms, organizations, government, consultants, academia, etc.) in the development and use of methods to manage innovation in a knowledge-driven economy. The paper identifies the main innovation management techniques (IMTs) aiming at the improvement of firm competitiveness by means of knowledge management. It will specifically focus on those IMTs for which knowledge is a relevant part of the innovation process. The research study, based on a survey at the European level, concludes that a knowledge-driven economy affects the innovation process and approach. The traditional idea that innovation is based on research (technology-push theory) and interaction between firms and other actors has been replaced by the current social network theory of innovation, where knowledge plays a crucial role in fostering innovation. Simultaneously, organizations in both public and private sectors have launched initiatives to develop methodologies and tools to support business innovation management. Higher education establishments, business schools and consulting companies are developing innovative and adequate methodologies and tools, while public authorities are designing and setting up education and training schemes aimed at disseminating best practices among all kinds of businesse

Sound and Complete Typing for lambda-mu

In this paper we define intersection and union type assignment for Parigot's calculus lambda-mu. We show that this notion is complete (i.e. closed under subject-expansion), and show also that it is sound (i.e. closed under subject-reduction). This implies that this notion of intersection-union type assignment is suitable to define a semantics.Comment: In Proceedings ITRS 2010, arXiv:1101.410

APPLICATION DES SONDES A FAISCEAU ELECTRONIQUE AUX MESURES LOCALES DE CONCENTRATIONS ET DE TEMPERATURES DE ROTATION

L'article traite des effets d'environnement sur la précision des mesures de masse volumique, et de l'emploi du modèle de Smith pour les mesures de température de rotation.The paper deals with the environment effects on the accuracy of the density measurements, and the use of the Smith model to the rotational temperature measurement