Exploitable results Types and computations Type theory and the proof theory of nonclassical logic provide the basis for most of the current theoretical research in functional programming languages. These mathematical tools have been useful in establishing connections and mutual enrichment with object-oriented (OO) languages and algebraic approaches to programming theory, type theories and models for functional programming, syntactic and semantic problems raised by parametricity in higher-order type theory and polymorphic languages; mathematical models for type theories with parametric-type disciplines and for feasible computations, OO programming; new tools for the design of OO languages based on type systems and logic; reasoning about (higherorder) programming language constructs. With the purpose of integrating functional and OO styles, an analysis will be carried out of languages containing polymorphic functions and abstract data type declarations, proof theory of non-classical logic (linear, modal), and a suitable Curry-Howard isomorphism for modal proofs. Results: Vladimir Sazonov developed the theory of feasible computable functions, partly on models of typed lambda-systems as proposed by Ershov and Scott. These systems establish an original connection between Logic and Computer Science and require a non-trivial mathematical insight. In particular, it was possible to relate models for type-free computations, higher order functionals and full-abstraction for a paradigmatic functional programming language, LCF. This analysis of full abstraction was a recent fall-out of the project and probably the main application. V. Kistlerov and S. Baranoff considered more practical problems, mostly related to concrete programming languages (FLAC, by Kistlerov, and FORTH, by S. Baranoff), with possible generalizations (e.g., generalization of backtracking and other features, in particular form Object Oriented programming). FLAC is an Object Oriented, extended during the project to handle pattern matching. Ongoing work should lead to some original form of type-inference, as the traditional ones cannot be applied to the current frame. FORTH is a "stack-oriented" language (more in the style of Java): stack manipulation has been implemented as well as a "graphically described" form of backtracking. Longo developed various research activities in applied logic and its philosophical counterpart (also in relation to cognitive sciences); his role in this project was essentially a co-ordinating activity. A full account of Longo's work may be obtained from his web pages : http://www.botik.ru/~logic/SAZONOV/papers.html Searching for OpenAIRE data... There was an error trying to search data from OpenAIRE No results available
