I am looking for motivated students and postdocs interested in the topics below. The city and the scientific context are nice.
UFR Sciences et Techniques
2, rue de la Houssinière, BP 92208
44322 Nantes Cedex 3
- Participez aux Journées Nationales Géocal-LAC 2017, les 13 et 14 novembre à Nantes !
- September 2017: I present a talk entitled “What term assignments can do for focusing” at the Fourth Meeting on Structures and Deduction (SD 2017). (Abstract)
- June 2017: a note on models of polarised intuitionistic logic arising from ones of linear logic. (HAL).
- May 2017: a note on Curry's style for Linear Call-by-Push-Value (HAL).
- April 2017: I present a talk entitled “Duploid situations in concurrent games”, joint work with Pierre Clairambault, at the GaLoP 2017 workshop. (Abstract)
- Feb 2016: I present the paper A Theory of Effects and Resources: Adjunction Models and Polarised Calculi, joint work with Marcelo Fiore and Pierre-Louis Curien, at the 43rd annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 2016).
- June 2015: The paper, Polarised Intermediate Representation of Lambda Calculus with Sums, joint work with Gabriel Scherer, to be presented at the Thirtieth Annual ACM/IEEE Symposium on Logic In Computer Science (LICS 2015), is available on HAL.
- July 2014: I have appended the proofs from my PhD thesis referred to in my paper Formulae-as-Types for an Involutive Negation, accepted for the Joint meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (CSL-LICS).
- June 2014: The slides for the first part of my talk entitled Polarities and classical constructiveness, at the Institut Henri Poincaré thematic trimester on Semantics of proofs and certified mathematics, are available. For the second part, see my talk at FOSSACS.
- February 2014: The LaTeX package perfectcut.sty is now hosted on CTAN and is available via TeXLive and MiKTeX.
- July 9th 2012: added to the note Λ-calcul, machines et orthogonalité a comparison of Krivine's “adapted pairs” technique to the orthogonality technique.
I am interested in proof theory, programming language theory, category theory, and the connections between them. In my view, the Curry-Howard correspondence is an active methodology as much as a foundation. The discovery of similar structures between proofs and programs reveals that there are similar phenomena at work in logic and computation; our work is then to explain these phenomena by developing paradigms, where mathematical abstractions play a crucial role of unification and fertilisation.
In this view, the λ-calculus is a successful and established paradigm of higher-order computation. It takes many forms, such that the paradigm cannot be reduced to a particular formalism. My research focuses on more expressive settings, often featuring “evaluation order”, where the paradigm of the λ-calculus has shown many limitations. In these contexts, one has repeatedly discovered the same structures since the 1960's: so-called “dualities of computation” observed in various topics (operational, categorical and game semantics, the proof theory of classical logic, and proof search). They display a further (“Gentzen-Landin”) correspondence and call for a unifying paradigm of evaluation order, whose current inadequacy is witnessed by idiosyncrasies in our fields. My publications contribute to such a paradigm.
This plays a role in various topics that keep me busy currently:
- Proof-theoretical coherence,
- Type theory with evaluation order,
- Axiomatics of type systems and denotational semantics,
- Applications of higher-order rewriting,
- Resource management in programming languages.
- Guillaume Combette
- Xavier Montillet