Research objectives and content
The reliability of the functional programming languages is a consequence of the deep understanding we have gotten about the meaning of paradigmatic functional programs. The Curry-Howard Isomorphism or ''Formulas (of Intuitionistic Logic)as-Types' is a milestone of such understanding. The Curry-Howard Isomorphism was extended to intensional aspects of the functional programs as soon as Linear Logic was introduced. However, the intensional information, collected by the formulas of Linear Logic, is not exactly the same as the intensional description of functional computations, expressed by I the Geometry of Interaction.
This project is about looking for a logical system for Geometry of Interaction. This means to find a logic such that its formulas are sets of (suitable) processes which interact by asking and answering questions. The main point of introducing a ''Formulas-as-Processes' paradigm is to exploit the modularity of types. This allows to program with processes, which express intensional features of the functional computations, exactly as we do with functional programs.
Training content (objective, benefit and expected impact)
Objective: Geometry of Interaction is an algebraic tool to express the intensional aspects of the functional computations from a fairly general perspective. The aim is looking for a logical system which formulas formalize invariant properties of the intensional information about computation that Geometry of Interaction makes evident.
Benefit: The 'Formulas-as-Types' discipline on abstract functional programs suggested to develop reliable functional languages. Analogous benefits, though at a different level, are expected by using the paradigm ''Types-as-Processes (described by Geometry of Interaction).' The level the benefits show up relates to the problems of better implementing functional languages on existing architectures and to propose new architectures.
Expected impact: Theoretically, the project contributes to make the ''Formulas-as-Processes (described by Geometry of Interaction)' paradigm as stable as the analogous ''Formulas-as-Types' for functional programs. Practically, the project influences the design of better implementations of functional languages, exploiting the modularity of types. Links with industry / industrial relevance (22)