I am a Research Fellow in the School of Computer Science at the University of Birmingham, and part of the Theory of Computation research group. I work with Vincent Rahli on the project: Design and Verification of Time-Critical Byzantine Fault-Tolerant Systems.
I did my DPhil (PhD) in Computer Science at the University of Oxford, supervised by Samson Abramsky. Before this, I spent a couple of years across the pond completing an MS in Logic, Computation and Methodology at Carnegie Mellon University, Pittsburgh. My first degree was an MSci in Physics and Philosophy from the University of Bristol.
I was born in Hexham, Northumberland, and grew up in Lichfield, Staffordshire. I am married to Julia. I like circket (especially a crisp cover drive), music (especially playing the piano) and food (especially cheese).
s.l.speight at bham.ac.uk
Office 242
School of Computer Science
University of Birmingham
B15 2TT
UK
News
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Research
Keywords: type theory, category theory, realizability, distributed systems
Computation: Often, "computation" is taken to mean those actions that could be carried out by a machine, though it is interesting to note that original conception of "computer" was a human being following strict and unambiguous rules.
Language and logic: For a given domain, can we capture and reason about it in a natural and convenient way?
Structure: How are things put together? What sort of inference does a particular structure support?
These interests manifest in the study of type theory and category theory. Category theory is the mathematics of structure (or even the mathematics of mathematics—mathematics is all about structure, right?); it studies classes of objects and transformations between them. Type theories are formal languages, like logics, but where proofs (as in mathematics) and programs (as in computing) live as first-class citizens. In fact, programs are proofs (this is part of the "Curry-Howard correspondence"). Type theories are implemented in so-called "proof assistants", which aid mathematicians in writing proofs, and can be used for the verification of programs.
Categorical models can be used to prove things about type theories (such as consistency and independence results). Conversely, type theories provide "internal languages" for reasoning about/inside structured categories. The basic objects of a type theory may behave natively like objects that are otherwise complicated to construct; we say that type theory lets us reason synthetically about such objects.
In homotopy type theory (HoTT), where they can be multiple identifications between two objects, we can reason synthetically about spaces.I mostly work on categorical realizability models. Realizability reveals computational content in mathematical proofs. Moreover, it provides models of dependent and impredicative type theories. I have developed an approach to realizability models of HoTT in which realizers (computations) themselves carry the structure of a space (or groupoid).
Papers
S. Speight. Groupoidal realizability for intensional type theory. Mathematical Structures in Computer Science: Advances in Homotopy Type Theory, 2024. doi:10.1017/S0960129524000343.
S Awodey, J. Frey, S. Speight. Impredicative encodings of (higher) inductive types. LICS 2018. doi:10.1145/3209108.3209130.
Theses
Higher-Dimensional Realizability for Intensional Type Theory. PhD thesis, University of Oxford (supervised by Samson Abramsky), 2023. Available here.
Impredicative encodings of inductive types in homotopy type theory Master's thesis, Carnegie Mellon University (supervised by Steve Awodey and Jonas Frey), 2017. Available here.
Talks
Computing up to isomorphism: proof-relevant PERs
Réalisabilité, CIRM, April 2025, slides
Computation up to isomorphism: higher-dimensional realizability
Dame Kathleen Ollerenshaw annual workshop: Categorical Logic and Higher Categories, University of Manchester, December 2024, slides
Proof-relevant partial equivalence relations
6th SMLS, Oxford, June 2024, slides
Partial combinatory algebras for intensional type theory
ACT 2024, Oxford, slides, recording
TYPES 2024, Copenhagen, extended abstract
Groupoidal realizability over cubical lambda-calculus
HoTT 2023, CMU, slides
Higher-dimensional realizability for intensional type theory
CMU HoTT Seminar, November 2022
Groupoidal realizability: formalizing the topological BHK interpretation of intensional type theory
LoVe Seminar, University of Paris 13, May 2022
Logic and Higher Structures, CIRM, February 2022
Impredicative encodings of (higher) inductive types
LICS 2018, Oxford
Encoding inductive types in impredicative intensional dependent type theory
Invited talk at Practical and Foundational Aspects of Type Theory, University of Kent, June 2018
Teaching
As instructor:
The Nature of Mathematical Reasoning, CMU, Summer 2016 and Spring 2017
As tutor/TA/grader:
Models of Computation, Oxford (Wycliffe Hall), Michaelmas 2021
Categories, Proofs and Processes, Oxford (Computer Science), Michaelmas 2019 and 2020
Formal Logic, CMU, Fall 2016
Ethical Theory, CMU, Spring 2016
Engineering Ethics, CMU, Fall 2015
Stuff
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