## Section: New Results

### Effects in proof theory and programming

Participants : Kostia Chardonnet, Emilio Jesús Gallego Arias, Hugo Herbelin, Yann Régis-Gianas, Alexis Saurin, Exequiel Rivas Gadda.

#### A theory of effects and resources

In collaboration with Thomas Letan (ANSSI), Yann Régis-Gianas developed and proved several properties of a simple web server implemented in Coq using FreeSpec. This work will be presented at CPP 2020.

#### Call-by-need with probabilistic effects

As a follow up of Chardonnet's Master 1 internship, Kostia Chardonnet and Alexis Saurin continued investigating call-by-need calculi extended with probabilistic choice and started preliminary discussions with Claudia Faggian.

#### Proof-search, algebraically and graphically

Alexis Saurin worked on proof search in a proof-net scenario, that is proof-net search. A key aspect of proof construction is a management of non-determinism in bottom-up sequent-proof construction, be it when the search succeeds or when facing a failure and the need for backtracking. This is partially dealt with by focussing proof-construction, which reduces drastically the search space while retaining completeness of the resulting proof space (both at the provability level and at the denotational level).

His approach consists in viewing proof-search and sequentialisation as dual aspects of partial proof structures (that is proof nets with open premisses). In particular, he builds on Lafont's parsing criterion to obtain a proof-construction algorithm in which the proof space is not a search tree, as in sequent-calculus, but a dag allowing to share proof-construction paths.

Emilio Jesús Gallego Arias collaborates with Jim Lipton from Wesleyan University on the development of algebraic models for proof search.