Intensional Partial Metric Spaces

8 June 2016
Steve Matthews

Partial metric spaces generalise metric spaces by allowing self-distance
to be a non-negative number. Originally motivated by the goal to
reconcile metric space topology with the logic of computable functions
and Dana Scott's innovative theory of topological domains they are now
too rigid a form of mathematics to be of use in modelling contemporary
applications software (aka 'Apps') which is increasingly concurrent,
pragmatic, interactive, rapidly changing, and inconsistent in nature.
This talks aims to further develop partial metric spaces in order to
catch up with the modern computer science of 'Apps'. Our illustrative
working example is that of the 'Lucid' programming language,and it's
temporal generalisation using Wadge's 'hiaton'.

  • Analytic Topology in Mathematics and Computer Science