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.