Section: New Results

Effects in proof theory and programming

Participants : Hugo Herbelin, Yann Régis-Gianas, Alexis Saurin, Exequiel Rivas Gadda.

Interfaces for computational effects

Exequiel Rivas studied the relation between interfaces for computational effects in programming languages: arrows, idioms and monads. Building on previous results of Lindley, Yallop and Wadler, a categorical account was developed by means of monoidal adjunctions. This work was presented in MSFP 2018 [40] and later in SYCO I. Together with Ruben Pieters and Tom Schrijvers, a journal version of the article is currently being prepared that includes this work and previous work on non-monadic handlers. It will be submitted to the Journal of Functional Programming.

Monads with merging

In collaboration with Mauro Jaskelioff, Exequiel Rivas developed monads with merge-like operators. These operators are based on two well-known algebraic theories for concurrency: classic process algebras and the more recent concurrent monoids. This resulted in an article submitted to FoSSaCS.

Relative effects: coherence for skew structures

In joint work with Mauro Jaskelioff, Tarmo Uustalu and Niccolò Veltri, Exequiel Rivas developed coherence theorems in the setting of categories with skew structures: skew monoidal categories, skew near-rig categories, skew semigroup categories. These skew structures are motivated by the study of relative effects in programming languages, where the primary example are relative monads. The results are formalised in the programming language Agda. A journal article is currently being written.

Effectful proving

Hugo Herbelin started a program of reconstruction of different levels of computational strength of logic by means of translation to a core logic of polarised linear connectives.

On the computational strength of choice axioms

With the goal of transferring the effectful computational contents of the dependent choice to other forms of choice or bar induction axioms, Hugo Herbelin worked at clarifying the folklore regarding the strengths of various forms of choice and of bar induction.

In collaboration with Boban Velickovic, Alexis Saurin advised the LMFI master internship of Ikram Cherigui on classical realisability and forcing in set theory.

Effectful systems in Coq

In collaboration with Thomas Letan (Agence Nationale pour la Sécurité des Systèmes Informatiques), Pierre Chifflier (ANSSI) and Guillaume Hiet (Centrale Supélec), Yann Régis-Gianas developed a new approach to model and verify effectful systems in Coq. This work has been presented at FM 2018 [38].