## Section: New Results

### Incrementality

Participants : Thibaut Girka, Yann Régis-Gianas.

#### Incrementality in proof languages

In collaboration with Paolo Giarrusso, Philipp Shuster and Yufei Cai (Univ Marburg, Allemagne), Yann Régis-Gianas developed a new method to incrementalise higher-order programs using formal derivatives and static caching. Yann Régis-Gianas has developed a mechanised proof for this transformation as well as a prototype language featuring efficient derivatives for functional programs. A paper has been submitted to ESOP 2019.

In collaboration with Olivier Martinot (Paris Diderot), Yann Régis-Gianas studied a new technique to implement incrementalised operations on lists. A paper is to be submitted to ICFP 2019.

#### Difference languages

Kostia Chardonnet and Yann Régis-Gianas started the formalisation of difference languages for Java, using the framework developed by Thibaut Girka. In particular, Kostia Chardonnet implemented a mechanised small step operational semantics for a large subset of Java. A paper is in preparation.