## Section: Research Program

### Proof checking

A thesis, which is at the root of our research effort, and which was
already formulated in [31], is that proof checkers should be theory
independent. This is for instance expressed in the title of our
invited talk at ICALP 2012: *A theory independent Curry-De
Bruijn-Howard correspondence* [30]. Such a theory independent proof checker
is called a logical framework.

Part of our research effort is focused on improving the λΠ-calculus modulo theory, for instance allowing to define congruences with associative and commutative rewriting.

Another part of our research effort is focused on the automatic analysis of theories to prove their confluence, termination, and consistency automatically [3].