Tom de Jong
Postdoc at the University of Nottingham working on type theory. PhD from the University of Birmingham. Mathematician, computer scientist and runner.
Postdoc at the University of Nottingham working on type theory. PhD from the University of Birmingham. Mathematician, computer scientist and runner.
There are just a few days left now to register for the Midlands Graduate School (MGS) in Sheffield, 7-11 April 2025. Eight fantastic courses on category theory, type theory, coalgebra, semantics and more.
Registration closes on Monday 24th March.
A *gentle* reminder that, I have a funded #PhD position for UK students, available with myself and @bentnib
This project will be looking at developing new methods for asserting the resilience of existing communicating systems by developing new static analysis methods derived from advanced programming language research.
Deadline for getting in contact is: Thursday 20th March 2025
You will belong to @StrathCyber and @mspstrath, as well as gaining access to @spli
—Abstract—
Motivated by the study of weak identity structures in higher category theory we explore the fat Delta category, a modification of the simplex category introduced by J. Kock. We provide a comprehensive study of fat Delta via the theory of monads with arities, and use these results to show that fat Delta is a hypermoment category in the sense of C. Berger. Specifically, by proving that the free relative semicategory monad is strongly cartesian and identifying a dense generator, the theory of monads with arities immediately gives rise to the nerve theorem. We characterise the essential image of the nerve via the Segal condition, and show that fat Delta possesses an active-inert factorisation system. Building on these results, we also establish an isomorphism between two presentations of fat Delta and show that it is a strongly unital and extensional hypermoment category.
I am very proud of our PhD student @Stiephen Pradal whose first paper appeared on the arXiv today! 🎉
https://arxiv.org/abs/2503.10963
In this paper we study the fat Delta category, a modification of the simplex category introduced by Joachim Kock. A full abstract can be found in the reply to this post.
Stiéphen's also finishing up a second (single authored) paper on a presentation of fat Delta via generators and relations, so stay tuned for more!
@squads Thanks! Same website as in the original post. (I'll make another post about it when they're up.)
@ToucanIan Same website as in the original post. (I'll make another post about it when they're up.)
Many thanks to everyone who attended and made this an amazing day of #logic, #computabilitytheory and #categorytheory!
Recordings and slides will be available on the website sometime next week (hopefully)!
This question is inspired by recent discussions with @dwarn.
It is well-known that univalence (the statement that the canonical map A = B → A ≃ B is an equivalence) implies function extensionality (see the HoTT book §4.9, this blog post by Dan Licata, or @MartinEscardo's formalisation of Voevodsky's proof).
It's also well-known (see here) that univalence is equivalent to the existence of a function ua : A ≃ B → A = B with a computation rule
uaβ : ∀ (e : A ≃ B) → transport (ua e) = e .fst
But it seems like this computation rule already bakes in some kind of function extensionality, since it produces an equality between functions. What happens if we make the computation rule "pointwise" instead?
uaβ' : ∀ (e : A ≃ B) (a : A) → transport (ua e) a = e .fst a
This is clearly equivalent to univalence if we assume funext, but it doesn't seem to imply funext. All the proofs I mentioned above seem to rely crucially on the fact that uaβ gives an equality of functions at some point.
My (admittedly cursed) question, then: is there a model of intensional type theory that validates this "pointwise" form of univalence, but not function extensionality?
The number of submissions for TYPES 2025 over time; aka "academics once again procrastinate until just before the deadline"
2-Coherent Internal Models of Homotopical Type Theory
Joshua Chen
https://arxiv.org/abs/2503.05790 https://arxiv.org/pdf/2503.05790 https://arxiv.org/html/2503.05790
arXiv:2503.05790v1 Announce Type: new
Abstract: The program of internal type theory seeks to develop the categorical model theory of dependent type theory using the language of dependent type theory itself. In the present work we study internal homotopical type theory by relaxing the notion of a category with families (cwf) to that of a wild, or precoherent higher cwf, and determine coherence conditions that suffice to recover properties expected of models of dependent type theory. The result is a definition of a split 2-coherent wild cwf, which admits as instances both the syntax and the "standard model" given by a universe type. This allows us to give a straightforward internalization of the notion of a 2-coherent reflection of homotopical type theory in itself: namely as a 2-coherent wild cwf morphism from the syntax to the standard model. Our theory also easily specializes to give definitions of "low-dimensional" higher cwfs, and conjecturally includes the container higher model as a further instance.
As part of our (@sarantja@mastodon.social and yt) research on the usability of interactive theorem provers, we are conducting a study on the usage and state of tools and languages for type-driven development. We are interested in tools that encourage and facilitate type-driven development, especially in cases when they can help us reason about complex problems.
We are hoping to use your responses to identify the characteristic language features and tool interactions that enable type-driven development, with the eventual goals of enhancing them and bringing their benefits to a wider range of programmers.
Please fill in our anonymous, 10-minute survey here: https://tudelft.fra1.qualtrics.com/jfe/form/SV_bIsMxYTKUJkhVuS
You are welcome to participate if you have experience with any type-driven development tool, including dependently-typed languages (e.g., Coq, Lean, Agda), refinement types (e.g., Liquid Haskell), or even other static type systems (e.g., in Rust or Haskell).
P.S. In case you remember signing up for an interview with us in a previous survey and are now wondering whether that study will still go on, the answer is: yes! We’ve had to revise our schedule, but we are still excited to talk to you and will start inviting people for an interview soon.
#Agda #Coq #Rocq #Lean #LiquidHaskell #Rust #Haskell #TypeDrivenDevelopment #TyDe #DependentTypes #LiquidTypes #RefinementTypes #ProofAssistants #Survey
Given it’s international women’s day, I’d like to encourage you all, but especially Dutch men to read these ‘anti-acknowledgments’ in a PhD thesis. This is not from somewhere else, it’s from Delft. And it’s not from the 1950s, but from the present. Unfortunately what academic life and culture in The Netherlands is still like. The author is just one of the few who actually spoke up about it, but there are many stories like it.
(Alt at https://pastebin.com/cqLvxX1f)
Folks, you (or rather... we as I've finally started mine) still have a last few days to put a TYPES abstract together!
2 pages, excluding bibliography
I'm excited to be teaching an advanced course on categorical realizability at this school!
If you're interested, please see the notes for my course at the Midlands Graduate School last year: https://github.com/tomdjong/MGS-categorical-realizability
36th European Summer School in Logic, Language and Information
https://2025.esslli.eu/
Registration is now open for students!
Boosts are appreciated.
Next Wednesday (12th March), Birmingham will host the 9th Southern and Midlands Logic Seminar (SMLS), with talks from Nicolai Kraus, Sonia Marin, Nick Hu and Maria Osório, with another talk to be announced shortly.
https://toddwaughambridge.co.uk/smls9
If you'd like to attend, please drop me a quick email (link on the above webpage), and if applicable add any dietary/accessibility requirements. We should be able to cover travel expenses!
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