Objectives(Super)deduction modulo is a formalism [DHK01,DHK03] in which deduction steps are seperated from computational steps. Besides its philosophical interest, this distinction allows to reduce the size of proofs (as showed in [Bur07]) by transfering the algorithmic part of a proof into a congruence defined by rewriting rules. This formalism allows to deduce the coherence and witness properties directly from the cut elimination property.
The project focusses on the development of an universal proof checker called Dedukti. It is based on the application of principles of (super)deduction modulo to type theory [CD07]. The development of this tool requires:
- to obtain theoritical results for examples for the encoding of proofs from Coq (Calculus of Inductive Constructions formalism) in Dedukti (lambda Pi-calculus modulo formalism)
- to develop implementation techniques for a successful scale-up.
The first release of Dedukti is now available.
In the current state, the computation of the rewriting systems to encode theories (or inference systems) is not automatic. In this project, we want to extend the work of [BK09] based on completion, to contribute to this automatisation. In this context, it could be useful to have powerful termination techniques (using for example the techniques presented in [BR09]).
We do not restrict ourselves to proof assistants based on type theory but we are also using the proof assistant Lemuridae [BHK07] making explicit a proof term language for superduction modulo and providing as interactive construction of proof terms like in Coq. The originality of Lemuridae is that it is based on the classical sequent calculus, allowing thus to expore non-deterministic calculus as well as proof search.
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