## Section: New Results

### Computation with meta-variables

Participant : Stéphane Lengrand.

Meta-variables are central in proof search mechanisms to represent incomplete proofs and incomplete objects. They are used in almost all implementations of proof software, yet their meta-theory remains less explored than that of complete proofs and objects such as the -calculus.

Stéphane Lengrand and Jamie Murdoch Gabbay have studied an extension of -calculus with a particular kind of meta-variables originating from nominal logic. A paper on this study is in revision phase for a publication in Information and Computation.

The highlight of 2008 is the design of a typing system with polymorphism
*à la* Hindley-Milner, as used in programming languages like CaML. The extension of
-calculus with meta-variables creates particular difficulties for the typing algorithm to be implemented in the compiler. A deciding algorithm for typing is being developed using constraints and graph theory.