Section: Partnerships and Cooperations

European Initiatives

FISP: ANR blanc International

Participants : Kaustuv Chaudhuri, François Lamarche, Sonia Marin, Dale Miller, Lutz Straßburger.

• Title: The Fine Structure of Formal Proof Systems and their Computational Interpretations

• Duration: 01/01/2016 – 31/10/2019

• Partners:

  • University Paris VII, PPS (PI: Michel Parigot)

  • Inria Saclay–IdF, EPI Parsifal (PI: Lutz Straßburger)

  • University of Innsbruck, Computational Logic Group (PI: Georg Moser)

  • Vienna University of Technology, Theory and Logic Group (PI: Matthias Baaz)

• Total funding by the ANR: 316 805 EUR

The FISP project is part of an ambitious, long-term project whose objective is to apply the powerful and promising techniques from structural proof theory to central problems in computer science for which they have not been used before, especially the understanding of the computational content of proofs, the extraction of programs from proofs and the logical control of refined computational operations. So far, the work done in the area of computational interpretations of logical systems is mainly based on the seminal work of Gentzen, who in the mid-thirties introduced the sequent calculus and natural deduction, along with the cut-elimination procedure. But that approach shows its limits when it comes to computational interpretations of classical logic or the modelling of parallel computing. The aim of our project, based on the complementary skills of the teams, is to overcome these limits. For instance, deep inference provides new properties, namely full symmetry and atomicity, which were not available until recently and opened new possibilities at the computing level, in the era of parallel and distributed computing.

COCA HOLA: ANR JCJC Project

Participant : Beniamino Accattoli.

• Title: COst model for Complexity Analyses of Higher-Order programming LAnguages.

• Collaborators: Ugo Dal Lago (University of Bologna & Inria), Delia Kesner (Paris Diderot University), Damiano Mazza (CNRS & Paris 13 University), Claudio Sacerdoti Coen (University of Bologna).

• Duration: 01/10/2016 – 31/09/2019

• Total funding by the ANR: 155 280 EUR

The COCA HOLA project aims at developing complexity analyses of higher-order computations, i.e. that approach to computation where the inputs and outputs of a program are not simply numbers, strings, or compound data-types, but programs themselves. The focus is not on analysing fixed programs, but whole programming languages. The aim is the identification of adequate units of measurement for time and space, i.e. what are called reasonable cost models. The problem is non-trivial because the evaluation of higher-order languages is defined abstractly, via high-level operations, leaving the implementation unspecified. Concretely, the project will analyse different implementation schemes, measuring precisely their computational complexity with respect to the number of high-level operations, and eventually develop more efficient new ones. The goal is to obtain a complexity-aware theory of implementations of higher-order languages with both theoretical and practical downfalls.

The projects stems from recent advances on the theory of time cost models for the lambda-calculus, the computational model behind the higher-order approach, obtained by the principal investigator and his collaborators (who are included in the project).

COCA HOLA will span over three years and is organised around three work packages, essentially:

1. extending the current results to encompass realistic languages;

2. explore the gap between positive and negative results in the literature;

3. use ideas from linear logic to explore space cost models, about which almost nothing is known.