#### Barbara Petit (Equipe Sardes, INRIA Grenoble)

#### LiDeAl: Certifying complexity with Linear Dependent Types

Dependant Linear PCF (dlPCF) was introduced by Dal Lago and Gaboardi as a type system characterising the complexity of PCF programs. It is parametrised by a an equational program, which is used to express some complexity annotations for types. This enables a modular complexity analysis, and the main strength of the system is to be relatively complete: any terminating PCF program is typable in dlPCF (and its complexity is thus determined) assuming that the equational program is expressive enough.

We have designed a type inference algorithm for this system: given a PCF program, it computes its type in dlPCF (and thus a complexity bound for the program) together with a set of proof obligations that ensures the correctness of the type, following the same scenario as the computation of weakest preconditions in Hoare logic. Checking formally the proof obligations generated by the type checker then amounts to a formal proof that the complexity bound is correct.

In this talk I will explain how the type system dlPCF can be turned into a tool for formal certification of the complexity of functional programs.