This research project is organised in various parts which correspond to the main areas of interest and to possible interaction among the various sites. In some cases joint collaboration has already been achieved.

Type theory and the proof theory of non-classical 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 (higher-order) 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.

Other topics will include an extension of Lawvere's quantifiers are adjoints to modal quantifiers, full isomorphisms between natural deduction proofs, modal lambda terms, arrows of suitable categories and a language for computer algebra.
The language FLAC has been already designed and implemented by one of the Russian participants. Further investigation is required to develop its functional features and its mathematical semantics.