## Section: New Software and Platforms

### Dedukti

Dedukti is a proof-checker for the $\lambda \Pi $-calculus modulo. As it can be parametrized by an arbitrary set of rewrite rules, defining an equivalence relation, this calculus can express many different theories. Dedukti has been created for this purpose: to allow the interoperability of different theories.

Dedukti's core is based on the standard algorithm for type-checking semi-full pure type systems and implements a state-of-the-art reduction machine inspired from Matita's and modified to deal with rewrite rules.

Dedukti's input language features term declarations and definitions (opaque or not) and rewrite rule definitions. A basic module system allows the user to organize his project in different files and compile them separately.

The new version of Dedukti (v2.5) brings two major improvements.

First the typing of rewrite rules has been completely reworked. It can now check a large class of rewrite rules including rules whose left-hand sides are not algebraic nor well-typed. Moreover the typing context do not need to be given with the rewrite rule anymore, as it is inferred by Dedukti, and therefore it is more convenient for the user.

Second, Dedukti can now be interfaced with automatic confluence checkers in order to check that the rewrite system generated by the rewrite rules together with beta reduction is confluent. This verification is important as the soundness of the program relies on this hypothesis.