Is the exponential function computable? Are union and intersection of closed subsets of the
real plane computable? Are differentiation and integration computable operators? Is zero …

This book serves as an introduction to an area of computability theory that originated in the
1950s, and since then has fanned out in many different directions under the influence of …

The goal of this article is to summarise the first steps in developing a fundamentally new way
of constructing theories of physics. The motivation comes from a desire to address certain …

Synthetic topology as conceived in this monograph has three fundamental aspects:(i) to
explain what has been done in classical topology in conceptual terms,(ii) to provide one …

An interval is a continuum of real numbers, defined by its end-points. Interval analysis,
proposed by R. Moore in the 50's, concerns the discovery of interval functions to produce …

Stable partial metric spaces form a fundamental concept in Quantitative Domain Theory.
Indeed, all domains have been shown to be quantifiable via a stable partial metric. Monoid …

In this dissertation, I explore aspects of computable analysis and topology in the framework
of relative realizability. The computational models are partial combinatory algebras with …

We give a domain-theoretic semantics to a statistical programming language, using the plain
old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably …

We study a programming language with a built-in ground type for real numbers. In order for
the language to be sufficiently expressive but still sequential, we consider a construction …

Real PCF is an extension of the programming language PCF with a data type for real
numbers. Although a Real PCF definable real number cannot be computed in finitely many …