Postdoc at the University of Nottingham working on type theory. PhD from the University of Birmingham. Mathematician, computer scientist and runner.
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2026-05-03T05:29:18Z Event JSON
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Last Notes npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong On my way to Gothenburg for #TYPES. Please come and say hi! npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong With apologies for the delay, the recordings of the talks at the Types and Topology Workshop in celebration of @nprofile…t6k2's 60th birthday (https://tdejong.com/mhe60) are now on YouTube (where available) 📺 https://www.youtube.com/@mhe60/videos (also linked from the workshop webpage) Many thanks to all speakers once again! #TypeTheory #ConstructiveMath npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…xuzd As the owner of this weird computer I retract my earlier claim about typst and automatic transitions. (But I still don't know what happened, sorry.) @nprofile…r0xq npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong Together with @nprofile…yjy4 and Simona Paoli, I'm organizing the 112th Peripatetic Seminar on Sheaves and Logic (PSSL 112) in Nottingham on 28—29 March 2026. https://sites.google.com/view/pssl112/ Talks at PSSL cover all areas of #CategoryTheory and its applications. If you'd like to contribute, please submit a one-page abstract (not counting references, in pdf) to [email protected] by 6 February 2026 (Friday next week). Thanks! npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…xuzd I take it you won't tell us? 🙃 npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong —Abstract— It is known that, in univalent mathematics, type universes, the type of n-types in a universe, reflective subuniverses, and the underlying type of any algebra of the lifting monad are all (algebraically) injective. Here, we further show that the type of ordinals, the type of iterative (multi)sets, the underlying type of any pointed directed complete poset, as well as the types of (small) ∞-magmas, monoids, and groups are all injective, among other examples. Not all types of mathematical structures are injective in general. For example, the type of inhabited types is injective if and only if all propositions are projective. In contrast, the type of pointed types and the type of non-empty types are always injective. The injectivity of the type of two-element types implies Fourman and Ščedrov's world's simplest axiom of choice. We also show that there are no nontrivial small injective types unless a weak propositional resizing principle holds. Other counterexamples include the type of booleans, the simple types, the type of Dedekind reals, and the type of conatural numbers, whose injectivity implies weak excluded middle. More generally, any type with an apartness relation and two points apart cannot be injective unless weak excluded middle holds. Finally, we show that injective types have no non-trivial decidable properties, unless weak excluded middle holds, which amounts to a Rice-like theorem for injective types. @nprofile…t6k2 npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong I'm pleased that my paper with @nprofile…t6k2 on (counter)examples of injective types is out on arXiv: https://arxiv.org/abs/2601.12536. This paper took a while to come together, partly because we refined the exposition a few times, partly because we kept coming up with new (counter)examples, and partly because we formalized (nearly) everything in TypeTopology using Agda. But that's okay, because I'm confident that all of these things led to a better paper. [Abstract in the next post] #TypeTheory #Agda npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong The University of Nottingham just enabled Outlook's archive feature: “To keep your mailbox lighter and faster, emails that are older than 90 days are automatically moved into an online archive. You will find your old emails in the following folder: - In the Outlook app, the folder name is: Online Archive – [Your Name] - In the web version of Outlook, the folder name is: In-Place Archive [Your Name]” In practice this means I can no longer access any emails older than 90 days in Thunderbird and there does not appear to be an option to download the In-Place Archive. My question: What can I do to get this archive into Thunderbird, or to at least retain an offline copy? I tried following https://stackoverflow.com/questions/28005516/can-you-use-davmail-to-access-exchange-archives and https://unix.stackexchange.com/questions/179034/can-i-view-my-microsoft-exchange-online-archive-via-davmail-in-thunderbird but that didn't work. (In particular Thunderbird flat out refuses to add an account with the same server and username...) #Outlook #Thunderbird #FediTips #IMAP npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong The slides for Types and Topology (https://tdejong.com/mhe60) are all up on the website now (where available)! @nprofile…w8t5 npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…rrqe For those wondering what's happening in Birmingham: https://tdejong.com/mhe60/ 🙂 npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong I'm happy that my proposal for an introductory course on Homotopy Type Theory / Univalent Foundations at the European Summer School in Logic, Language and Information 2026 in Prague was accepted! A great opportunity to make use of @nprofile…356e's recently published book, @nprofile…w8t5's lecture notes (in Agda!) and @nprofile…v38n and @nprofile…9t3n's book draft! Links for the curious: - Egbert's book: https://doi.org/10.1017/9781108933568 & https://arxiv.org/abs/2212.11082 - Martín's notes: https://cs.bham.ac.uk/~mhe/HoTT-UF-in-Agda-Lecture-Notes/index.html - Daniel and Carlo's book draft: https://www.danielgratzer.com/papers/type-theory-book.pdf #logic #typetheory npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong Junk email: "I came across your preprint titled "On Small Types in Univalent Foundations" [...] Your manuscript aligns well with the following journal: Journal of Rare Cardiovascular Diseases" These diseases must indeed be extremely rare if univalent foundations are relevant... 😂 npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…w8t5 is turning 60 this year! In celebration, Eric Finster and I are organizing a two-day workshop on 17-18 December 2025 at the University of Birmingham. https://tdejong.com/mhe60 The full list of over 20 invited speakers can be found on the website and reflects Martín's diverse contributions to constructive mathematics, domain theory, locale theory, logic, topology and homotopy/univalent type theory. The workshop is co-located with the Midlands Graduate School (MGS) Christmas Seminar on 16 December 2025 and will support remote participation. If you would like to attend (in person or remotely), please register by *21 November 2025* by completing this form: https://forms.cloud.microsoft/e/4GgaZHTxad npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong The extended version of our LICS'25 paper, titled Constructive Ordinal Exponentiation, is now on arXiv. It has two new sections (Section 6 and 8) on ordinal arithmetic. Everything is formalized in Agda and merged into @nprofile…w8t5's TypeTopology repository. https://arxiv.org/abs/2501.14542v5 This joint work with @nprofile…qrru, @nprofile…jy82 and Chuangjie Xu. #TypeTheory #logic #Agda npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong Following the Heyting Day symposium held in honour of Jaap van Oosten, Benno van den Berg and I wrote a brief popular article on Jaap's life, his scientific work (categorical realizability) and his other contributions to academic life. Jaap has done a great deal for mathematical logic in the Netherlands, and in Utrecht in particular, and we are extremely grateful to him for his efforts! The article is publicly available here: https://www.nieuwarchief.nl/serie5/pdf/naw5-2025-26-3-176.pdf #logic #mathematics #maths #math npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong Back from holiday and just caught up on @nprofile…6kk0's very interesting HoTTEST talk titled "Is it time for a new proof assistant?" https://www.youtube.com/watch?v=7oBkEbKJvnE #typetheory npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong PhD position with Benno van den Berg on the semantics of Homotopy Type Theory (esp. effective Kan fibrations) at the ILLC in Amsterdam! https://www.illc.uva.nl/NewsandEvents/News/Positions/newsitem/15777/PhD-Position-in-the-Semantics-of-Homotopy-Type-Theory Application deadline: 27 September. #math #maths #computerscience #phd #HoTT #TypeTheory npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…6kk0 This basic fact is indeed surprisingly tricky to prove. I think I would follow @nprofile…hszg's approach which goes via Hedberg's argument https://martinescardo.github.io/HoTT-UF-in-Agda-Lecture-Notes/HoTT-UF-Agda.html#subsingletonsaresets. npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…6kk0 @nprofile…2pts @nprofile…hszg explained something similar in this thread: https://mathstodon.xyz/@MartinEscardo/114717657709706036 npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong My paper "Continuous and algebraic domains in univalent foundations" with @nprofile…hszg was accepted for publication by the Journal of Pure and Applied Algebra! 🎉 https://martinescardo.github.io/papers/continuous-algebraic-domains-in-uf.pdf This paper has its origin in my very first paper with Martín (and my second paper overall) "Domain Theory in Constructive and Predicative Univalent Foundations" which appeared at Computer Science Logic (CSL) back in 2021. Since then I wrote my PhD thesis on this topic (and worked on other things in type theory after) and the present paper is both a revision of the CLS'21 paper and my PhD thesis (which I completed in 2022). Everything in the paper has been formalized and an HTML rendering of the Agda file that directly links the code to the paper can be found here: https://martinescardo.github.io/TypeTopology/DomainTheory.Continuous-and-algebraic-domains.html #typetheory #agda #logic #math #computerscience npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong It was both a pleasure and a privilege to deliver 5 90-min blackboard (!) lectures on Categorical Realizability to 20–30 students and fellow lecturers at the European Summer School in #Logic, Language and Information (#ESSLLI). I really enjoyed the interaction with all attendees and appreciated their excellent questions and comments: thank you! Also, a huge thanks to @nprofile…56vx and the other organizers for running #ESSLLI2025 so smoothly!! npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong On my way to Bochum to teach a course on Categorical Realizability at the European Summer School in #Logic, Language and Information 😄 #esslli2025 #esslli npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…v2av "When you say "Next I will do X" or "Now I will do Y" or "I will do X", you MUST actually do X or Y instead just saying that you will do it. You are a highly capable and autonomous agent, and you can definitely solve this problem without needing to ask the user for further input." 😂😂😂 npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong This short expository paper has now been published (https://doi.org/10.4230/LIPIcs.TYPES.2024.1) along with the other papers of the TYPES 2024 post-proceedings 🎉 #typetheory npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…v2av I think the HoTT book did a good job at gently introducing infomal UF. As for your second question: yes, people do write papers in informal UF, e.g. any of @nprofile…hszg's papers (or my own for that matter) where the setting is UF. Not sure if this is a pitfall, but the main thing to be careful about (and which UF forces you to be) is the distinction between property and data, and Sigma and exists. npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…6kk0 Do you have slides you can share? npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong TYPES talk done! Time to enjoy the rest of the conference 😄 I talked about injective types in univalent mathematics which is joint work with @nprofile…hszg. You can find my slides here https://tdejong.com/talks/TYPES-2025.pdf. #TYPES2025 #typetheory #HoTT npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…hszg @nprofile…kkfd There's also the book by Roy Crole, but I haven't read any of it, so I can't say anything more about it really. npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong The recordings and slides of the contributed and invited talks from the Workshop on Homotopy Type Theory/Univalent Foundations (HoTT/UF) are all up at https://hott-uf.github.io/2025/ Thanks again to all our speakers! npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…6kk0 Great, thank you! I'm looking forward to studying this when I'm finished with my ITP reviews... npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…6kk0 Congratulations to all of you! After our discussions, I'm keen to see what you and Leoni did! Will that paper be on arXiv soon? npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong I'm happy to report that my expository note (https://arxiv.org/abs/2408.11501), which has previously been kindly mentioned on here by @nprofile…w52t and @nprofile…6kk0, has been accepted to the TYPES 2024 post-proceedings 🙂 #typetheory #formalization npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong 36th European Summer School in Logic, Language and Information https://2025.esslli.eu/ Registration is now open for students! Boosts are appreciated. #logic #computerscience npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong Call for Papers 16th International Conference on Interactive Theorem Proving — ITP'25 Reykjavik, Iceland 27 September – 3 October 2025 https://icetcs.github.io/frocos-itp-tableaux25/itp/ ITP is concerned with all aspects of interactive theorem proving, ranging from theoretical foundations to implementation aspects and applications in program verification, security, and the formalization of mathematics. - Abstract submission deadline: 12 March 2025 - Paper submission deadline: 19 March 2025 - Author notification: 23 May 2025 - Camera-ready copy due: 27 June 2025 #formalization #theoremproving #proofassistants #verification #CfP npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…wksm @nprofile…6kk0 I think @nprofile…hszg advises all his PhD students to read this (at least he did to me). npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong @nprofile…6kk0 When I was creating semi-automated marking scripts for Functional Programming (Haskell) assignments, I always had to remember to test for the empty list separately, as many students would forget about it and would fail complete tests just because of the empty list. npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong The Dutch #Categories and #Types Seminar (https://DutchCATS.github.io) yesterday was great fun! The slides for my talk "Ordinal Exponentiation in Homotopy Type Theory" are here: https://tdejong.com/talks/DutchCATS-2025-02-07.pdf npub1mfshurh4s2j74g8hwpama06jqxhzg00h7lmmwhy56253zdh5dujqmu8tlu Tom de Jong —Abstract— While ordinals have traditionally been studied mostly in classical frameworks, constructive ordinal theory has seen significant progress in recent years. However, a general constructive treatment of ordinal exponentiation has thus far been missing. We present two seemingly different definitions of constructive ordinal exponentiation in the setting of homotopy type theory. The first is abstract, uses suprema of ordinals, and is solely motivated by the expected equations. The second is more concrete, based on decreasing lists, and can be seen as a constructive version of a classical construction by Sierpiński based on functions with finite support. We show that our two approaches are equivalent (whenever it makes sense to ask the question), and use this equivalence to prove algebraic laws and decidability properties of the exponential. All our results are formalized in the proof assistant Agda.