GLC actors, artificial chemical connectomes, topological issues and knots

Based on graphic lambda calculus, we propose a program for a new model of asynchronous distributed computing, inspired from Hewitt Actor Model, as well as several investigation paths, concerning how one may graft lambda calculus and knot diagrammatics

Deduction modulo theory

This paper is a survey on Deduction modulo theor

Relational Parametricity and Control

We study the equational theory of Parigot's second-order λμ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equivalence on the λμ-terms. On the other hand, the unconstrained relational parametricity on the λμ-calculus turns out to be inconsistent with this CPS semantics. Following these facts, we propose to formulate the relational parametricity on the λμ-calculus in a constrained way, which might be called ``focal parametricity''.Comment: 22 pages, for Logical Methods in Computer Scienc

Linear-algebraic lambda-calculus

With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an interpreter/simulator) is provided for this language in the form of a term rewrite system. The linear-algebraic lambda-calculus hereby constructed is linear in a different (yet related) sense to that, say, of the linear lambda-calculus. These various notions of linearity are discussed in the context of quantum programming languages. KEYWORDS: quantum lambda-calculus, linear lambda-calculus, $\lambda$-calculus, quantum logics.Comment: LaTeX, 23 pages, 10 figures and the LINEAL language interpreter/simulator file (see "other formats"). See the more recent arXiv:quant-ph/061219

Introducing a Calculus of Effects and Handlers for Natural Language Semantics

In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the same pattern: they are instances of a monad. In this paper, we present an extension of the simply-typed lambda calculus that exploits this uniformity using the recently discovered technique of effect handlers. We prove that our calculus exhibits some of the key formal properties of the lambda calculus and we use it to construct a modular semantics for a small fragment that involves multiple distinct semantic phenomena