2020-05-29: Dominic Orchard (University of Kent)

Sat, 21 Oct 2023 21:24:08 +0100

Dominic Orchard (University of Kent)

The 'graded types' paradigm: past, present, and a possible future

Abstract

In the 1970s, the notion of 'grading' appeared in analytic philosophy and logic as a way of making reasoning more fine-grained, capturing 'degrees' of necessity or possibility. Somewhat independently, grading has become a topic of interest in type theory and programming language semantics, with graded structures again providing a means of more fine-grained reasoning. In this talk, I will give an overview of this idea (both its past and present) and explore two uses: (1) using graded modal types for program reasoning in the context of an experimental functional language with linear and indexed types, called Granule; (2) specialising program semantics to give correct-by-construction arguments about program analyses and transformations. I will also give a mathematical characterisation of grading which suggests a broad paradigm, and will briefly mention various ongoing works.

2020-05-29 11:00:00 UTC
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