Philip Scott, better known to his friends and colleagues as Phil, was a Professor of
Mathematics at the University of Ottawa (Canada). Sadly, Phil passed away1 after a long …

Control flow of quantum programs is often divided into two different classes: classical and
quantum. Quantum programs with classical control flow have their conditional branching …

Notions of guardedness serve to delineate the admissibility of cycles, eg in recursion,
corecursion, iteration, or tracing. We introduce an abstract notion of guardedness structure …

This paper deals with questions relating to Haghverdi and Scott's notion of partially traced
categories. The main result is a representation theorem for such categories: we prove that …

Quantum algorithms are sequences of abstract operations, performed on non-existent
computers. They are in obvious need of categorical semantics. We present some steps in …

Haghverdi introduced the notion of unique decomposition categories as a foundation for
categorical study of Girardʼs Geometry of Interaction (GoI). The execution formula in GoI …

Aspects of Categorical Recursion Theory Page 1 Aspects of Categorical Recursion Theory
Pieter Hofstra and Philip Scott Abstract We present a survey of some developments in the …

This paper revisits the theory of compact affine semigroups and monoids, an area of intense
research activity in earlier phases of compact semigroup theory. We outline the basic …

We present Geometry of Interaction (GoI) models for Multiplicative Polarized Linear Logic,
MLLP, which is the multiplicative fragment of Olivier Laurent's Polarized Linear Logic. This is …

A denotational semantics of quantum Turing machines having a quantum control is defined
in the dagger compact closed category of finite dimensional Hilbert spaces. Using the Moore …