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## Section: New Results

### Tight Typings and Split Bounds

Participants : Beniamino Accattoli, Stéphane Graham-Lengrand.

This joint work with Delia Kesner (Paris Diderot University) [12] 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 ICFP 2018.

Intersection types are a classic tool in the study of the $\lambda$-calculus. They are known to characterise various termination properties.

It is also well-known that multi types, a variant of intersection types strongly related to linear logic, also characterise termination properties. Typing derivation of multi types, moreover, provide quantitative information such as the number of evaluation step and the size of the results, as first shown by de Carvalho.

In this work we provide some new results on this line of work, notably we provide the first quantitative study via multi types of the leftmost and linear head evaluation strategies. Moreover, we show that our approach covers also the other cases in the literature.