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 Design and Verification of Time-Critical Byzantine Fault-Tolerant Systems project.
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
...
Research
Keywords: type theory, category theory, realizability, distributed systems
Computation: I study the scope and limits of computation. Often, "computation" is taken to mean those actions that a machine could carry out (with enough resources), though it is interesting to note that original conception of "computer" was a human being following fixed 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 (sometimes called the mathematics of mathematics—well, mathematics has to do with is about structure, right?); it studies classes of objects and transformations between them. Type theories are formal languages, like logics, though in type theory, proofs (as in mathematics) and programs (as in computing) live within the language as first-class citizens. Proofs and programs are actually the same kind of thing in type theory; this is part of the "Curry-Howard correspondence". Type theories are implemented in so-called "proof assistants" (such as Agda and Coq), which aid mathematicians in writing proofs, whilst simultaneously acting as programming languages.
Categorical models can be used to prove things about type theories (such as consistency results). Conversely, type theories provide "internal languages" for reasoning about/inside structured categories. The basic objects of a type theory may behave like particular objects that are otherwise complicated to encode; we say that type theory lets us reason synthetically about such objects.
The flavour of categorical model that much of my work to date has focused on is realizability models. Realizability reveals computational content of mathematical theories, and provides models of dependent and impredicative type theories. For my PhD, I developed higher-dimensional realizability models of intensional type theory based on groupoids, wherein realizers themselves carry higher-dimensional structure.
Papers
Impredicative encodings of (higher) inductive types
With Steve Awodey and Jonas Frey.
LICS 2018. doi:10.1145/3209108.3209130
Theses
Higher-Dimensional Realizability for Intensional Type Theory
PhD thesis, University of Oxford, supervised by Samson Abramsky.
Impredicative encodings of inductive types in homotopy type theory
Master's thesis, Carnegie Mellon University, supervised by Steve Awodey and Jonas Frey.
Available here.
Talks
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
Stuffs
...