Logic Seminar - Philip Saville
| Dates: | 20 May 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Philip Saville (University of Sussex)
Title: Semantic models for functions, via logic and universal algebra.
Abstract: It turns out that ideas from logic and universal algebra can be very useful for studying both the semantics of programming languages --- their model theory --- and the algebraic structures they form. The aim of this talk is to give a flavour of this, taking as my 'programming language' an extremely simple calculus which has functions and nothing else (i.e. simply-typed lambda calculus, but without products). First we shall see how structures like sets-and-functions give sound, but not complete, models. Then we’ll see two ways of giving models that are both sound and complete. The first uses certain abstract clones, a notion from universal algebra, while the second draws on the relationship between lambda calculus and combinatory logic, and has interesting connections to closed categories.
This will be something of a whistlestop tour, and I will try to keep it mostly self-contained. In particular, I won't assume any prior knowledge of lambda calculus, combinatory logic, or categories.
Related paper: https://arxiv.org/abs/2405.01675 arxiv.org.
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3.9
Roscoe Building
Manchester
