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Section: New Results

Coq as a functional programming language

Participants : Pierre Boutillier, Guillaume Claret, Lourdes Del Carmen González Huesca, Hugo Herbelin, Pierre Letouzey, Matthias Puech, Yann Régis-Gianas, Matthieu Sozeau.

Type classes and libraries

Type Classes are heavily used in the HoTT/Coq library (http://github.com/HoTT/coq ) developed by the Univalent Foundations program at the IAS, to which Matthieu Sozeau participated.

Dependent pattern-matching

How to encode structurally dependent pattern matching into case analysis by hand has been described by Jean François Monin in [52] . Pierre Boutillier, with the help of Thomas Braibant (GALLIUM team), has mechanized this process and exhibited a missing part to make it scale. These are the main results presented in Pierre Boutillier's forthcoming thesis.

Incrementality in proof languages

Lourdes González and Yann Régis-Gianas studied incremental computing and self-adjusting computation  [24] as a starting point to develop an applicative notion of change over data structures, to be applied to lambda-terms. They formalized in Coq a notion of derivative of an inductive function to define how to compute a new result from an input that has changed, this is done by using the derivative of the function and the difference on inputs and old outputs. They are working out a technique that allows a specification of functions using derivatives and old inputs and outputs including a cost analysis of the benefits of reusing previous computations.

Lightweight proof-by-reflection

In collaboration with Beta Ziliani (MPI), In the context of the ANR project Paral-ITP, Lourdes del Carmen González Huesca, Guillaume Claret and Yann Régis-Gianas developed a new technique for proof-by-reflection based on a notion of a posteriori simulation of effectful computations in Coq. This work has been presented at ITP 2013 ([14] ).