Semantics of a Typed Algebraic Lambda-Calculus

Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We sketch the relation with two established vectorial lambda-calculi. Then we study the problems arising from the addition of a fixed point combinator and how to modify the equational theory to solve them. We sketch an algebraic vectorial PCF and its possible denotational interpretations

Innocent strategies as presheaves and interactive equivalences for CCS

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.Comment: In Proceedings ICE 2011, arXiv:1108.014

Lectures on Rings and Modules

VIII, 183 tr.; 23 cm

A non-distributive calculus of numerical functions.

[...] The distributive law, under which in any orthodox algebraic system, addition and multiplication enter into postulational wedlock, is absent from our calculus of numerical functions, even though many instances of it are true. We are thus compelled to investigate a novel variant of ordinary algebra, a system in which the distributive law does not necessarily hold. In want of a better name, we shall refer to such a system, subject to certain restrictions to be enumerated in § 2, as a calculus