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Section: Partnerships and Cooperations
International Initiatives
STRUCTURAL: ANR blanc International
Participants : Kaustuv Chaudhuri, Nicolas Guenot, Willem Heijltjes, Clément Houtmann, Dale Miller, Lutz Straßburger.
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Title: Structural and computational proof theory
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Duration: 01/01/2011 – 31/12/2013
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Partners:
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Total funding by the ANR: 242 390,00 EUR (including 12 000 EUR pôle de compétivité: SYSTEMTIC Paris région)
This project is a consortium of four partners, two French and two Austrian, all being internationally recognized for their work on structural proof theory, but each coming from a different tradition. One of the objective of the project is build a bridge between these traditions and develop new proof-theoretic tools and techniques of structural proof theory having a strong potential of applications in computer science, in particular at the level of the models of computation and the extraction of programs and effective bounds from proofs.
On one side, there is the tradition coming from mathematics, which is mainly concerned with first-order logic, and studies, e.g., Herbrand's theorem, Hilbert's epsilon-calculus, and Goedel's Dialectica interpretation. On the other side, there is the tradition coming from computer science, which is mainly concerned with propositional systems, and studies, e.g., Curry-Howard isomorphism, algebraic semantics, linear logic, proof nets, and deep inference. A common ground of both traditions is the paramount role played by analytic proofs and the notion of cut elimination. We will study the inter-connections of these different traditions, in particular we focus on different aspects and developments in deep inference, the Curry-Howard correspondence, term-rewriting, and Hilbert's epsilon calculus. As a byproduct this project will yield a mutual exchange between the two communities starting from this common ground, and investigate, for example, the relationship between Herbrand expansions and the computational interpretations of proofs, or the impact of the epsilon calculus on proof complexity.
Besides the old, but not fully exploited, tools of proof theory, like the epsilon-calculus or Dialectica interpretation, the main tool for our research will be deep inference. Deep inference means that inference rules are allowed to modify formulas deep inside an arbitrary context. This change in the application of inference rules has drastic effects on the most basic proof theoretical properties of the systems, like cut elimination. Thus, much of the early research on deep inference went into reestablishing these fundamental results of logical systems. Now, deep inference is a mature paradigm, and enough theoretical tools are available to think to applications. Deep inference provides new properties, not available in shallow deduction systems, namely full symmetry and atomicity, which open new possibilities at the computing level that we intend to investigate in this project. We intend to investigate the precise relation between deep inference and term rewriting, and hope to develop a general theory of analytic calculi in deep inference. In this way, this project is a natural continuation of the ANR project INFER which ended in May 2010.
Eternal: INRIA ARC
Participants : Kaustuv Chaudhuri, Dale Miller, Lutz Straßburger.
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Title: Interactive Resource Analysis
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webpage: http://eternal.cs.unibo.it/
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INRIA principal investigator: Dale Miller
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INRIA Partner:
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INRIA Partner:
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Duration: 2011 - 2013
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This project aims at putting together ideas from Implicit Computational Complexity and Interactive Theorem Proving, in order to develop new methodologies for handling quantitative properties related to program resource consumption, like execution time and space. The task of verifying and certifying quantitative properties is undecidable as soon as the considered programming language gets close to a general purpose language. So, full-automatic techniques in general cannot help in classifying programs in a precise way with respect to the amount of resources used and moreover in several cases the programmer will not gain any relevant information on his programs. In particular, this is the case for all the techniques based on the study of structural constraints on the shape of programs, like many of those actually proposed in the field of implicit computational complexity. To overcome these limitations, we aim at combining the ideas developed in the linear logic approach to implicit computational complexity with the ones of interactive theorem proving, getting rid of the intrinsic limitations of the automatic techniques. In the obtained framework, undecidability will be handled through the system's user, who is asked not only to write the code, but also to drive the semi-automatic system in finding a proof for the quantitative properties of interest. In order to reduce the user effort and allow him to focus only on the critical points of the analysis, our framework will integrate implicit computational complexity techniques as automatic decision procedures for particular scenarios. Moreover, in order to be widely applicable, the modularity of the framework will permit to deal with programs written in different languages and to consider different computational resources. The kind of study proposed by this project has been almost neglected so far. Here, we aim at providing such a framework for both theoretic investigations and for testing in practice the effectiveness of the approach.
INRIA Associate Teams
RAPT
Participants : Beniamino Accattoli, Kaustuv Chaudhuri, Quentin Heath, Clément Houtmann, Dale Miller.
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Title: Computational logic systems
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INRIA principal investigator: Kaustuv Chaudhuri
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International Partner:
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International Partner:
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Duration: 2011 - 2013
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Many aspects of computation systems, ranging from operational semantics, interaction, and various forms of static analysis, are commonly specified using inference rules, which themselves are formalized as theories in a logical framework. While such a use of logic can yield sophisticated, compact, and elegant specifications, formal reasoning about these logic specifications presents a number of difficulties. The RAPT project will address the problem of reasoning about logic specifications by bringing together three different research teams, combining their backgrounds in type theory, proof theory, and the building of computational logic systems. We plan to develop new methods for specifying computation that allow for a range of specification logics (eg, intuitionistic, linear, ordered) as well as new means to reason inductively and co-inductively with such specifications. New implementations of reasoning systems are planned that use interactive techniques for deep meta-theoretic reasoning and fully automated procedures for a range of useful theorems.
Visits of International Scientists
Invited Researchers
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Alberto Momigliano, Associate Professor, University of Milan
24 - 28 January and 30 - 31 August.
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Vivek Nigam, Research Scientist, LMU, Munich, Germany.
26 April - 6 May.
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Chuck Liang, Professor, Hofstra University, NY, USA.
2 June - 1 July
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Gopalan Nadathur, Professor, University of Minnesota, MN, USA.
6 -10 June and 3 - 28 October.
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Elaine Pimentel, Associate Professor, Universidade Federal de Minas Gerais.
13 - 24 June.
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Brigitte Pientka, Associate Professor, McGill University, Montreal, Canada.
16 - 20 May.
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Alwen Tiu, Research Scientist, Australian National University.
22 - 26 August.
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Anupam Das, PhD Student, University of Bath, UK.
21 - 25 November 2011
Internships
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Andrew Cave, PhD student at McGill Univ., Montreal, Canada.
Internship during May – July 2011
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Salil Joshi, PhD student at Carnegie Mellon Univ., USA.
Internship during June – August 2011
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Chris Martens, PhD student at Carnegie Mellon Univ., USA.
Internship during June – August 2011
Participation In International Programs
The team has travel funds within the following international programs.
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PHC Germaine de Staël 2011: funding travel between Bern, Switzerland and INRIA.
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63.123 - 63ème CPCFQ: Commission permanente de coopération franco-québécoise: funding exchanges between the McGill and INRIA.
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INRIA-FAPEMIG: funding between INRIA and the Brazilian funding agency FAPEMIG located in the state of Minas Gerais.