This colloquium was organised to celebrate the 60th birthday of Giuseppe Longo. Some photos of the meeting can be found here.
The main research area Giuseppe Longo has been interested in concerns
syntactic and semantic properties of the "logical base" of functional
languages: Combinatory Logic, Lambdacalculus and their extensions.
However, he always investigated these topics in its broadest setting
which relates them to Recursion Theory, Proof Theory and Category
Theory.
In this perspective, Longo worked at some aspects of Recursion
Theory, Higher Type Recursion Theory, Domain Theory and Category Theory
as part of a unified mathematical framework for the theory and the
design of functional languages. In a sense, Longo has always been
mostly interested in the "interconnecting results" or "bridges" and
applications among different areas and to language design. He also
worked at the applications of functional approaches to ObjectOriented
programming. He is currently extending his interdisciplinary interests
to Philosophy of Mathematics and Cognitive Sciences.
A recent interdisciplinary project on Geometry and Cognition (started with the corresponding grant: "Géométrie et
Cognition", 1999  2002 with J. Petitot et B. Teissier), focused on the geometry of physical and biological
spaces. The developements of this project lead to a new initiative at DIENS,
in 2002, the setting up of the research team "Complexité et information
morphologiques" (CIM), centered on foundational problems in the interface
between Mathematics, Physics and Biology.
This colloquium tries to partially cover the various fields spanned by Giuseppe Longo research via
several talks given by some of the collegues he met during his quest.

 Speakers and talks (alphabetical order)

Henk Barendregt and Jan Willem Klop:
Nonleft linear reductions via infinitary lambda calculus
[Abstract]
In this paper we treat two cases where an infinitary treatment yields
interesting finitary results. (1) Adding nonleftlinear reduction
rules such as Dxx → x or the reduction rules for Surjective Pairing
to the lambda calculus yields nonconfluence, as was proved in Klop
[80] using some elaborate machinery involving standardization and
postponement of certain reductions. We show how an extension to the
infinitary lambda calculus, where Böhm trees can be directly treated
and rewritten as infinite terms, yields a simple and intuitive proof of
the correctness of these ChurchRosser counterexamples. (2) In
Barendregt [84] it is shown that Surjective Pairing is not definable in
lambda calculus. We show how this result can easily be obtained as a
corollary of Berry's Sequentiality Theorem, which itself can be proved
by an excursion to the infinitary lambda calculus.
Kim Bruce:
Modularity and Scope in ObjectOriented Languages
[Abstract]
Language designers for objectoriented languages have tended to use
classes as the main modularity boundaries for code. While Java includes
packages, they were not particularly well thoughtout and have lots of
flaws. However, the designers got very little flack for the weak design
because programmers don't use them very effectively. In this talk we
describe some useful properties of modularity and informationhiding
mechanisms in objectoriented languages and and present a language
design that supports these properties.
Luca Cardelli:
Artificial Biochemistry
[Abstract]
Chemical and biochemical systems are presented as collectives of
interacting stochastic automata: each automaton represents a molecule
that undergoes state transitions. This framework constitutes an
artificial biochemistry, where automata interact by the equivalent of
the law of mass action. We analyze several example systems and networks,
both by stochastic simulation and by ordinary differential equations.
PierreLouis Curien:
Computational selfassembly
[Abstract]
The object of this talk is to appreciate the computational limits
inherent in the combinatorics of the κcalculus, an applied
concurrent language originally meant as a visual and concise
notation for biological signalling pathways. We define a
compilation of κ into a language where interactions can
involve at most two agents at a time. That compilation is generic,
the blowup in the number of rules is linear in the total rule set
size, and the methodology used in deriving the compilation relies
on an implicit causality analysis. The correctness proof is given
in details, and correctness is spelt out in terms of the existence
of a specific weak bisimulation. Allowing some of the rules to be
reversible allows to avoid deadlocks.
Mariangiola Dezani :
Session Types for ObjectOriented Languages
[Abstract]
A session takes place between two parties; after establishing a connection,
We study the incorporation of session types into objectoriented languages
through MOOSE, a multithreaded language with session types, thread spawning,
iterative and higherorder sessions. Our design aims to consistently
integrate the objectoriented programming style and sessions, and to be able
to treat various case studies from the literature. We describe the design of
MOOSE, its syntax, operational semantics and type system, and develop a type
inference system. We discuss also two extensions: subtyping with bounded
quantification enhancing typeability and asynchronous communications enhancing
progress. (Joint work with Alex Ahern, Mario Coppo, Sophia Drossopoulou, Elena
Giachino, Dimitris Mostrous, and Nobuko Yoshida).
Abbas Edalat:
Recursively measurable sets and computable measurable sets
[Abstract]
In 1950's, N. A. Sanin introduced the notion of a recursively
measurable set of the real line with respect to the Lebesgue
measure. It turned out to be equivalent to a similar notion that
G. Kriesel and D. Lacombe had also developed. We have recently
introduced the notion of computable measurable set with respect to any
Borel measure on any locally compact second countable Hausdorff
space. This new notion combines both settheoretic and
measuretheoretic approximations. A computable measurable set is
approximated in the measure with a recursive sequence of basic open
sets, each containing the original set, and a recursive sequence of
basic closed sets, each contained in the original set. We show that a
recursively measurable set can be constructed up to a null set as the
limsup of its defining sequence of open sets. We then show that for
the Lebesgue measure on the real line, where recursively measurable
sets are defined, a computable measurable set is recursively
measurable but not vice versa. We also compare the resulting notions of
recursively measurable (Lebesgue integrable) functions and computable
measurable (Lebesgue integrable) functions.
JeanYves Girard:
Truth, modality, intersubjectivity
[Abstract]
Logic has so far been unable to cope with truth, witness
Tarki's "definition".
In a finite von Neumann algebra, e.g., the MurrayvN
hyperfinite factor, truth can be defined w.r.t. a
viewpoint, i.e., a maximal abelian subalgebra.
The modality "necessary" appears as the affirmation of truth.
Truth is therefore subjective, in the style of quantum measurement.
This calls for an intersubjective explanation of logic.
Furio Honsell and Gordon Plotkin:
On the βηcompleteness and expressiveness of some classes of combinatory algebras
[Abstract]
The question whether there exists a Scot continuous retract model
of βη is 25 years old, and still open! We discuss and solve
several variations of this problem such as the βηcompleteness
and expressiveness of various classes of combinatory models for various classes of FOL formulae.
Eugenio Moggi:
Category Theory and Lambda Calculus
[Abstract]
We give an overview of the categorytheoretic view of
models for the lambda calculus and related systems. Starting from the
seminal idea of Scott (models of the untyped lambdacalculus as
reflexive objects in a CCC), we review how models for other calculi
(e.g. combinatory logic and secondorder lambda calculus) have been
described in Category Theory, and the role of Giuseppe Longo on these
developments.
Mioara MugurSchächter:
On the patient quest of Giuseppe Longo for a general unity and coherence
[Abstract]
In these times of utterly parcelling specialization, views
stemming from a severe education of rigor and nevertheless rooted in
a deep perception of the powers of intuition and a universal curiosity
concerning the various forms of human thought, are extremely rare. Via two examples  of which one concerns the specificity of quantum mechanical probabilities with resect to classical ones and the question of determinism and the other one the relations between physics and biology  I shall argue
that Giuseppe Longo is developing such a view.
Thierry Paul:
Semiclassical analysis and sensitivity to initial data
[Abstract]
We will present several recent results concerning
the transition between quantum and classical mechanics, in the situation
where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be emphasized, and the long time evolution will show how the quantum nondeterminism and the classical chaotic sensitivity to initial conditions can be compared, and in a certain sense overlap. An analogy with computer sciences (numerical computation for partial differential equations) will also be discussed.
Jean
Petitot:
Neurogeometry and the origin of space.
[Abstract]
Recent experiments in neurophysiology enable to better understand the
processing of visual inputs by cortical primary visual areas. Global
properties of percepts, in the sense of Gestalt theory, are a consequence
of the functional architecture of these areas. We have shown that the f
unctional architecture of V1 implements the contact structure of the visual
plane. This explains many properties of the integration of local sense data
into global perceptual structures.
John Stewart:
Is "life" computable?
[Abstract]
Robert Rosen has proposed a theoretical definition of "life itself"
as "closure under efficient cause". He has further put forward the
conjecture that a model of "life", so defined, is not computable.
In this talk, I propose to present this conjecture, which is
controversial (but which has important consequences for attempts
to model "artificial life" in the computer); and to present also
some recent developments which, although they do not entirely settle
the controversy, represent a significant advance.

Thursday, June the 28th, 2007  Amphitheater 3 (number 31 on this map) 
14:00 – 14:10

Welcome

14:10 – 15:30

Session 1: Lessons from Logic and Physics
Mioara MugurSchächter:
On the patient quest of Giuseppe Longo for a general unity and coherence
JeanYves Girard:
Truth, modality, intersubjectivity

15:30 – 16:00

Coffee break

16:00 – 16:40

Session 2: Geometry and Cognition
Jean Petitot:
Neurogeometry and the origin of space

16:40 – 18:00

Session 3: Models and Categories
Eugenio Moggi:
Category Theory and Lambda Calculus
Martin Hyland:
Modelling the Impossible


Friday, June the 29th, 2007  Amphitheater A (number 4 on this map) 
09:00 – 10:20

Session 4: Lambda Calculus
Henk Barendregt and Jan Willem Klop:
Nonleft linear reductions via infinitary lambda calculus
Furio Honsell and Gordon Plotkin:
On the βηcompleteness and expressiveness of some classes of combinatory algebras

10:20 – 10:40

Coffee break

10:40 – 12:40

Session 5: Theoretical Biology and Biological Theories
PierreLouis Curien:
Computational selfassembly
Luca Cardelli:
Artificial Biochemistry
John Stewart:
Is "life" computable?

12:40 – 14:00

Symposium lunch (provided)

14:00 – 15:20

Session 6: Types for ObjectOrientation
Mariangiola Dezani:
Session Types for ObjectOriented Languages
Kim Bruce:
Modularity and Scope in ObjectOriented Languages

15:20 – 15:40

Coffee break

15:40 – 17:00

Session 7: Analysis, Physics, and Recursion Theory
Abbas Edalat:
Recursively measurable sets and computable measurable sets
Thierry Paul:
Semiclassical analysis and sensitivity to initial data

17:00 – 17:50

Closing Talk
Giuseppe Longo:
From exact sciences to life phenomena: a few concluding
remarks on Bohr and Schrödinger


Venue, Registration, and Organisation

Informations about the venue, travel, organization, and registration are to be found in the
RDP 2007 page. The plan of the conference rooms is available here. Registration desk is located in the room "salle des textiles". 
