Coherence for Frobenius pseudomonoids and the geometry of linear proofs

We prove coherence theorems for Frobenius pseudomonoids and snakeorators in monoidal bicategories. As a consequence we obtain a 3d notation for proofs in nonsymmetric multiplicative linear logic, with a geometrical notion of equivalence, and without the need for a global correctness criterion or thinning links. We argue that traditional proof nets are the 2d projections of these 3d diagrams

Denotational, Causal, and Operational Determinism in Event Structures

Determinism is a theoretically and practically important concept in labelled transition systems and trees. We study its generalisation to event structures. It turns out that the result depends on what characterising property of tree determinism one sets out to generalise. We present three distinct notions of event structure determinism, and show that none of them shares all the pleasant properties of the one concept for trees

Pictures of complete positivity in arbitrary dimension

Two fundamental contributions to categorical quantum mechanics are presented. First, we generalize the CP-construction, that turns any dagger compact category into one with completely positive maps, to arbitrary dimension. Second, we axiomatize when a given category is the result of this construction.Comment: Final versio

Coherence for Star-Autonomous Categories

This paper presents a coherence theorem for star-autonomous categories exactly analogous to Kelly's and Mac Lane's coherence theorem for symmetric monoidal closed categories. The proof of this theorem is based on a categorial cut-elimination result, which is presented in some detail.Comment: 28 page

The Common HOL Platform

The Common HOL project aims to facilitate porting source code and proofs between members of the HOL family of theorem provers. At the heart of the project is the Common HOL Platform, which defines a standard HOL theory and API that aims to be compatible with all HOL systems. So far, HOL Light and hol90 have been adapted for conformance, and HOL Zero was originally developed to conform. In this paper we provide motivation for a platform, give an overview of the Common HOL Platform's theory and API components, and show how to adapt legacy systems. We also report on the platform's successful application in the hand-translation of a few thousand lines of source code from HOL Light to HOL Zero.Comment: In Proceedings PxTP 2015, arXiv:1507.0837