## Section: New Results

### Towards a link between CPS and focusing

Participant : Matthias Puech.

Continuation-passing style translations make a functional program more explicit by sequentializing its computations and reifying its control. They have been used as an intermediate language in many compilers. They are also understood as classical-to-intuitionistic proof embedding (so-called double negation translations). Matthias Puech studied a novel correspondence between CPS and focusing: to each CPS transform corresponds a focused proof system that is identifiable as a particular polarization of classical statements. Since, after Miller's and others work, we know the full design space of focused sequent calculi, we expect to understand the full design space of CPS translation.

The first step of this goal is to study the syntax and typing of variants of the CPS translation. Puech designed and implemented in OCaml a compacting, optimizing CPS translation, while using OCaml's type system to verify that it maps well-typed terms to well-typed terms in a tightly restricted syntactical form (the “typeful” approach to formalization) [82]. The resulting type system is in Curry-Howard isomorphism with a weakly focused proof system: LJQ.