Section: Overall Objectives
The aim of the Parsifal team is to develop and exploit the theories of proofs and types to support the specification and verification of computer systems. To achieve these goals, the team works on several level.
The team has expertise in proof theory and type theory and conducts basic research in these fields: in particular, the team is developing results that help with the automation of deduction and with the formal manipulation and communication of proofs.
Based on experience with computational systems and theoretical results, the team designs new logical principles, new proof systems, and new theorem proving environments.
Some of these new designs are appropriate for implementation and the team works at developing prototype systems to help validate basic research results.
By using the implemented tools, the team can develop examples of specifications and verification to test the success of the design and to help suggest new logical and proof theoretic principles that need to be developed in order to improve one's ability to specify and verify.
The foundational work of the team focuses on the proof theory of classical, intuitionistic, and linear logics making use, primarily, of sequent calculus and deep inference formalisms. A major challenge for the team is the reasoning about computational specifications that are written in a relational style: this challenge is being addressed with the introduction of some new approaches to dealing with induction, co-induction, and generic judgments. Another important challenge for the team is the development of normal forms of deduction: such normal forms can be used to greatly enhance the automation of search (one only needs to search for normal forms) and for communicating proofs (and proof certificates) for validation.
The principle application areas of concern for the team currently are in functional programming (e.g., -calculus), concurrent computation (e.g., -calculus), interactive computations (e.g., games), and biological systems.