Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators

The symmetric interaction combinators are an equally expressive variant of Lafont's interaction combinators. They are a graph-rewriting model of deterministic computation. We define two notions of observational equivalence for them, analogous to normal form and head normal form equivalence in the lambda-calculus. Then, we prove a full abstraction result for each of the two equivalences. This is obtained by interpreting nets as certain subsets of the Cantor space, called edifices, which play the same role as Boehm trees in the theory of the lambda-calculus

Semantics for a Quantum Programming Language by Operator Algebras

This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of the category of W*-algebras and normal completely positive subunital maps is an elementary quantum flow chart category in the sense of Selinger. As a consequence, it gives a denotational semantics for Selinger's first-order functional quantum programming language QPL. The use of operator algebras allows us to accommodate infinite structures and to handle classical and quantum computations in a unified way.Comment: In Proceedings QPL 2014, arXiv:1412.810

On Context Semantics and Interaction Nets

International audienceContext semantics is a tool inspired by Girard' s geometry of interaction. It has had many applications from study of optimal reduction to proofs of complexity bounds. Yet, context semantics have been defined only on $\lambda$-calculus and linear logic. In order to study other languages, in particular languages with more primitives (built-in arithmetic, pattern matching,...) we define a context semantics for a broader framework: interaction nets. These are a well-behaved class of graph rewriting systems. Here, two applications are explored. First, we define a notion of weight, based on context semantics paths, which bounds the length of reduction of nets. Then, we define a denotational semantics for a large class of interaction net systems

Applying quantitative semantics to higher-order quantum computing

Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the language to an unusably small finitary fragment, or giving up important features of quantum physics such as entanglement. In this paper, we propose a denotational semantics for a quantum lambda calculus with recursion and an infinite data type, using constructions from quantitative semantics of linear logic

Sequentiality vs. Concurrency in Games and Logic

Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc