Projecting games on hypercoherences

We compare two interpretations of programming languages : game
semantics (a dynamic semantics dealing with computational traces) and
hypercoherences (a static semantics dealing with results of
computation). We consider polarized bordered games which are Laurent’s
polarized games endowed with a notion of terminated computation (the
border) allowing for a projection on hypercoherences. The main result
is that the projection commutes to the interpretation of linear terms
(exponential-free proofs of polarized linear logic). We discuss the
extension to general terms.