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Section: New Results

Embeddings in the λΠ-calculus modulo

Ali Assaf has designed an embedding of the HOL logic in the λΠ-calculus modulo and implemented it in the HOLiDe system [40] .

Together with Mathieu Boespflug, Ali Assaf and Guillaume Burel have developed an embedding of the Calculus of Inductive Constructions with universes in the λΠ-calculus modulo and Ali Assaf is currently implementing it in a new version of the CoqInE system.

Catherine Dubois and Raphaël Cauderlier have studied a translation in the λΠ-calculus modulo of features coming from object oriented programming languages, such as inheritance and late binding. This compilation scheme has been applied to produce a new back-end for FoCaLize [8] , through a compilation to Dedukti. This new back-end is expected to be lighter than the present one producing Coq code and also to be able to combine local and external proofs coming from different proof environments [44] . They are currently working on a translation of the full FoCaLize language—not restricted to its object oriented features—and on a proof of its correctness with respect to the existing FoCaLize semantics.