## Section: New Results

### Types of Fireballs

Participant : Beniamino Accattoli.

This joint work with Giulio Guerrieri (Bologna University) [22] belongs to line of work *Cost Models and Abstract Machines for Functional Programs*, supported by the ANR project COCA HOLA, and it has been published in the proceedings of the international conference APLAS 2018.

The theory of the call-by-value $\lambda $-calculus has mostly been developed for *closed* programs, that is, programs without free variables. In the last few years, the authors dedicated considerable efforts to extend it to open terms, that is the case relevant for the implementation of proof assistants. The simplest presentation of the call-by-value $\lambda $-calculus for open terms is the *fireball calculus*.

In this work we extend the quantitative study via multi types mentioned in *Tight Typings and Split Bounds* to the fireball calculus.