Team Parsifal

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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 $ \lambda$ -calculus.

Stéphane Lengrand and Jamie Murdoch Gabbay have studied an extension of $ \lambda$ -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 $ \lambda$ -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.


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