Call-By-Push-Value from a Linear Logic Point of View

We present and study a simple Call-By-Push-Value lambdacalculus with fix-points and recursive types. We explain its connection with Linear Logic by presenting a denotational interpretation of the language in any model of Linear Logic equipped with a notion of embedding retraction pairs. We consider the particular case of the Scott model of Linear Logic from which we derive an intersection type system for our calculus and prove an adequacy theorem. Last, we introduce a fully polarized version of this calculus which turns out to be a term language for a large fragment of LLP and refines lambda-mu.