In memory of Gilles Kahn

The essence of this paper stems from discussions that the first author (Jean-Pierre Banâtre) had with Gilles on topics related with programming in general and chemical programming in particular. Gilles liked the ideas behind the Gamma model and the closely related Berry and Boudol's CHAM as the basic principles are so simple and elegant. The last opportunity Jean-Pierre had to speak about these ideas to Gilles, was when he presented the LNCS volume devoted to the Unconventional Programming Paradigms workshop. The 10 minutes appointment (at that time, he was CEO of INRIA) lasted a long time. Gilles was fine and in good humour, as often, and he was clearly happy to talk about a subject he loved. He spoke a lot about λ-calculus, the reduction principle, the β-reduction… a really great souvenir!

Abstract

Originally, the chemical model of computation has been proposed as a simple and elegant parallel programming paradigm. Data is seen as “molecules” and computation as “chemical reactions”: if some molecules satisfy a predefined reaction condition, they are replaced by the “product” of the reaction. When no reaction is possible, a normal form is reached and the program terminates. In this paper, we describe classical coordination mechanisms and parallel programming models in the chemical setting. All these examples put forward the simplicity and expressivity of the chemical paradigm.

Abstract

Grammars of natural languages are needed in programs such as natural language interfaces and dialogue systems, but also more generally, in software localization. Writing grammar implementations is a highly specialized task. For various reasons, no libraries have been available to ease this task. This paper shows how grammar libraries can be written in GF (Grammatical Framework), focusing on the software engineering aspects rather than the linguistic aspects. As an implementation of the approach, the GF Resource Grammar Library currently comprises ten languages. As an application, a translation system from formalized mathematics to text in three languages is outlined.

Introduction

How can we generate natural language text from a formal specification of meaning, such as a formal proof? Coscoy, Kahn and Théry studied the problem and built a program that worked for all proofs constructed in the Coq proof assistant. Their program translates structural text components, such as we conclude that, but leaves propositions expressed in formal language:

We conclude that Even(n) → Odd(Succ(n)).

A similar decision is made in Isar, whereas Mizar permits English-like expressions for some predicates. One reason for stopping at this level is certainly that typical users of proof systems are comfortable with reading logical formulas, so that only the proof-level formalization needs translation.

Foreword

This essay is dedicated in admiration to the memory of Gilles Kahn, a friend and guide for 35 years. I have been struck by the confidence and warmth expressed towards him by the many French colleagues whom he guided. As a non-Frenchman I can also testify that colleagues in other countries have felt the same.

I begin by recalling two events separated by 30 years; one private to him and me, one public in the UK. I met Gilles in Stanford University in 1972, when he was studying for the PhD degree – which, I came to believe, he found unnecessary to acquire. His study was, I think, thwarted by the misunderstanding of others. I was working on two different things: on computer-assisted reasoning in a logic of Dana Scott based upon domain theory, which inspired me, and on models of interaction – which I believed would grow steadily in importance (as indeed they have). There was hope to unite the two. Yet it was hard to relate domain theory to the non-determinism inherent in interactive processes. I remember, but not in detail, a discussion of this connection with Gilles. The main thing I remember is that he ignited. He had got the idea of the domain of streams which, developed jointly with David MacQueen, became one of the most famous papers in informatics; a model of deterministic processes linked by streams of data.

Abstract

Adjoint algorithms are a powerful way to obtain the gradients that are needed in scientific computing. Automatic differentiation can build adjoint algorithms automatically by source transformation of the direct algorithm. The specific structure of adjoint algorithms strongly relies on reversal of the sequence of computations made by the direct algorithm. This reversal problem is at the same time difficult and interesting. This paper makes a survey of the reversal strategies employed in recent tools and describes some of the more abstract formalizations used to justify these strategies.

Why build adjoint algorithms?

Gradients are a powerful tool for mathematical optimization. The Newton method for example uses the gradient to find a zero of a function, iteratively, with an excellent accuracy that grows quadratically with the number of iterations. In the context of optimization, the optimum is a zero of the gradient itself, and therefore the Newton method needs second derivatives in addition to the gradient. In scientific computing the most popular optimization methods, such as BFGS, all give best performances when provided gradients too.

In real-life engineering, the systems that must be simulated are complex: even when they are modeled by classical mathematical equations, analytic resolution is totally out of reach. Thus, the equations must be discretized on the simulation domain, and then solved, for example, iteratively by a computer algorithm.

Abstract

The split of a multihop, point-to-point TCP connection consists in replacing a plain, end-to-end TCP connection by a cascade of TCP connections. In such a cascade, connection n feeds connection n + 1 through some proxy node n. This technique is used in a variety of contexts. In overlay networks, proxies are often peers of the underlying peer-to-peer network. split TCP is also already proposed and largely adopted in wireless networks at the wired/wireless interface to separate links with vastly different characteristics. In order to avoid losses in the proxies, a backpressure mechanism is often used in this context.

In this paper we develop a model for such a split TCP connection aimed at the analysis of throughput dynamics on both links as well as of buffer occupancy in the proxy. The two main variants of split TCP are considered: that with backpressure and that without. The study consists of two parts: the first part is purely experimental and is based on ns2 simulations. It allows us to identify complex interaction phenomena between TCP flow rates and proxy buffer occupancy, which seem to have been ignored by previous work on split TCP. The second part of the paper is of a mathematical nature. We establish the basic equations that govern the evolution of such a cascade and prove some of the experimental observations made in the first part.

Introduction

I have spent 29 years of my life with INRIA. I had seen the beginning of the institute in 1967. I was appointed president of the institute in 1984 and I left it in 1996, after 12 years as president.

Gilles Kahn joined IRIA in the late 1960s and made his entire career in the institute. He passed away while he was president, after a courageous fight against a dreadful illness, which unfortunately did not leave him any chance. I knew him for more than 35 years and I have an accurate vision on the role he played in the development of the institute. More globally, I have seen his influence in the computer science community in France and in Europe. This article gives me the opportunity to understand what was behind such a leadership and to recall some of the challenges that INRIA has faced during more than three decades. What we can learn from the past and from the action of former great leaders is extremely helpful for the future.

This is probably the best way to be faithful to Gilles and to remain close to his thoughts.

Historical IRIA

Why IRIA?

INRIA was born as an evolution of IRIA.

IRIA was created in 1967 as a part of a set of decisions taken under the leadership of General de Gaulle. It was a time of bold decisions towards research at large, based on clear political goals.

Gilles Kahn was born in Paris on April 17th, 1946 and died in Garches, near Paris, on February 9th, 2006. He received an engineering diploma from Ecole Polytechnique (class of 1964), studied for a few years in Stanford and then joined the computer science branch of the French Atomic Energy Commission (CEA), which was to become the CISI company. He joined the French research institute in computer science and control theory (IRIA, later renamed INRIA) in 1976. He stayed with this institute until his death, at which time he was the chief executive officer of the institute. He was a member of Academia Europaea from 1995 and a member of the French Academy of Science from 1997.

Gilles Kahn's scientific achievements

Gilles Kahn's scientific interests evolved from the study of programming language semantics to the design and implementation of programming tools and the study of the interaction between programming activities and proof verification activities. In plain words, these themes addressed three questions. How do programmers tell a computer to perform a specific task? What tools can we provide to programmers to help them in their job? In particular, how can programmers provide guarantees that computers will perform the task that was requested?

Programming language semantics

In the early 1970s, Gilles Kahn proposed that programs should be described as collections of processes communicating through a network of channels, a description style that is now known as Kahn networks.

Abstract

We describe how the formal description of a programming language can be encoded in the Coq theorem prover. Four aspects are covered: Natural semantics (as advocated by Gilles Kahn), axiomatic semantics, denotational semantics, and abstract interpretation. We show that most of these aspects have an executable counterpart and describe how this can be used to support proofs about programs.

Introduction

Nipkow demonstrated in that theorem provers could be used to formalize many aspects of programming language semantics. In this paper, we want to push the experiment further to show that this formalization effort also has a practical outcome, in that it makes it possible to integrate programming tools inside theorem provers in an uniform way. We re-visit the study of operational, denotational semantics, axiomatic semantics, and weakest pre-condiction calculus as already studied by Nipkow and we add a small example of a static analysis tool based on abstract interpretation.

To integrate the programming tools inside the theorem prover we rely on the possibility to execute the algorithms after they have been formally described and proved correct, a technique known as reflection. We also implemented a parser, so that the theorem prover can be used as a playground to experiment on sample programs. We performed this experiment using the Coq system. The tools that are formally described can also be “extracted” outside the proof environment, so that they become stand alone programs.

Abstract

This paper presents a formal description of a small functional language with dependent types. The language contains data types, mutual recursive/inductive definitions and a universe of small types. The syntax, semantics and type system is specified in such a way that the implementation of a parser, interpreter and type checker is straight-forward. The main difficulty is to design the conversion algorithm in such a way that it works for open expressions. The paper ends with a complete implementation in Haskell (around 400 lines of code).

Introduction

We are going to describe a small language with dependent types, its syntax, operational semantics and type system. This is in the spirit of the paper “A simple applicative language: Mini-ML” by Clément, Despeyroux, and Kahn, where they explain a small functional language. From them we have borrowed the idea of using patterns instead of variables in abstractions and let-bindings. It gives an elegant way to express mutually recursive definitions. We also share with them the view that a programming language should not only be formally specified, but it should also be possible to reason about the correctness of its implementation. There should be a small step from the formal operational semantics to an interpreter and also between the specification of the type system to a type checker.

Introduction. We aim to use proof assistants (in our specific case Coq [9, 6]) to formally represent and reason about languages using higher-order syntax, i.e. object languages where binding operators are expressed using binding at the meta-level. This is an active and fertile field of research. Several methods contend to become the most elegant, efficient, and easy to use. The differences stem from the approach of the researchers and the characteristics of the proof tool used.

Our starting point was the work on the Hybrid tool in Isabelle/HOL by Ambler, Crole, and Momigliano [2].

Introduction. As van den Dries notes in his book [17], Grothendieck's dream of tame geometries found a certain realization in model theory, at first by the study of the geometric properties of definable sets for some nice structure like the field of real numbers, and then by axiomatizing these properties by notions of o-minimality, minimality, C-minimality, p-minimality, v-minimality, t-minimality, b-minimality, and so on. Although there is a joke speaking of x-minimality with x = a, b, c, d, …, these notions are useful and needed in different contexts for different kinds of structures, for example, o-minimality is for ordered structures, and v-minimality is for algebraically closed valued fields.

In recent work with F. Loeser [4], we tried to unify some of the notions of x-minimality for different x, for certain x only under extra conditions, to a very basic notion of b-minimality. At the same time, we tried to keep this notion very flexible, very tame with many nice properties, and able to describe complicated behavior.

An observation of Grothendieck's is that instead of looking at objects, it is often better to look at morphisms and study the fibers of the morphisms.