Andreas Nuyts

I am a postdoctoral fellow of the Research Foundation - Flanders (FWO) at imec-DistriNet, KU Leuven, Belgium. I obtained my PhD at this same university in August 2020, and have subsequently worked for 1 year at VUB.

Most of my research is about dependent type theory. There, I am interested in the theory and implementation of modal and presheaf type theory (particularly directed type theory), a quest which also led me to an interest in general syntactic aspects of type theory. I am also fascinated by the question of how to reason about side-effects in dependent type theory. Furthermore, I have been involved in a line of research, headed by Stelios Tsampas, on categorifying secure compilation.

I find it especially motivating to hear from people who are interested in (using) my work, so do not hesitate to contact me in case of questions, remarks or puzzlement about any of my papers, notes or code.

My research and publications

BibTeX - dblp - Google Scholar - ORCiD

Table of Contents

1. Posts
2. Syntax of Type Theory
3. Multimode and Presheaf Type Theory
4. Effects in Dependent Type Theory
5. Categorical Secure Compilation

Posts

• Equality-in-equality-out category theory in cubical Agda (Jul '22)

Syntax of Type Theory

Contextual Algebraic Theories: Generic Boilerplate beyond Abstraction (Accepted at TyDe '22)

• Extended Abstract - Slides* - Github

Understanding Universal Algebra Using Kleisli-Eilenberg-Moore-Lawvere Diagrams (2022)

• Note

Multimode and Presheaf Type Theory

Transpension: The Right Adjoint to the Pi-type (2021, Submitted to LMCS)
With Dominique Devriese.

• Preprint (based on ch. 7 of my PhD thesis) - Technical report
• Transpension: The Right Adjoint to the Pi-type (TYPES '22): Abstract - Slides*
• Dependable Atomicity in Type Theory (TYPES '19): Abstract - Slides*
• Internalizing Presheaf Semantics: Charting the Design Space (HoTT/UF '18): Abstract - Slides*

Sikkel: Multimode Simple Type Theory as an Agda Library (MSFP 2022)
By Joris Ceulemans, Andreas Nuyts, Dominique Devriese

• MSFP '22: DOI - Github - Slides* - Video
• TYPES '22: Abstract - Slides*

Extending Cubical Agda with Internal Parametricity (TYPES '22)
By Antoine Van Muylder, Andrea Vezzosi, Andreas Nuyts, Dominique Devriese

Abstract - Slides*

A Vision for Natural Type Theory (2020): Note

• Part I. Grothendieck Construction Considered Harmful
• Part II. Jets: Higher Equipments or Directed Degrees of Relatedness

Contributions to Multimode and Presheaf Type Theory (PhD thesis, 2020)
Supervisors: Dominique Devriese, Frank Piessens,
Committee chair: Robert Puers,
Other committee members: Lars Birkedal, Dan Licata, Bart Jacobs, Tom Schrijvers

• Overview (2022)
• Final version: in color - grayscale
  • Ch. 1 "Introduction",
    • Sec. 1.2 "Higher Directed Type Theory in Practice",
  • Ch. 5 "Multimode Type Theory",
  • Ch. 6 "Presheaf Type Theory",
  • Ch. 7 "Transpension: the Right Adjoint to the Π-type" is superseded by our LMCS submission,
  • Ch. 8 "Fibrancy" (Robust notions of contextual fibrancy),
  • Ch. 9 "Degrees of Relatedness",
    • Sec. 9.5 "Parametricity Features and their Requirements" is superseded by this note,
  • Ch. 10 "Conclusion"
    • Sec. 10.1.1 "Towards Higher Directed Type Theory",
      See also "A Vision for Natural Type Theory".
• Public defense: Slides* (for a general non-CS audience)
• Announcement for informed outsiders: English - Nederlands

• See ch. 8 of my PhD thesis.
• Abstract - Slides* (HoTT/UF '18)

• Journal paper (LICS special issue of LMCS '21)
• LICS paper (§5.3 of my PhD thesis) - Technical report

• Github
• Abstract - Slides* (TYPES '19)

• Paper with appendices - Official proceeding - Technical report
• Put in a more contemporary (2020) perspective in ch. 9 of my PhD thesis.
• Slides CHoCoLa @ ENS Lyon, Jan '19* (1h seminar: parametricity background, details of relation framework, model, structural modality, intersections and unions)
• Slides LICS '18* (focus on motivation - cuts straight to details of relation framework)
• Slides PLNL '18* (from System F parametricity to current work)
• Slides EUTypes meeting Nijmegen* (dated)

• Paper - DOI - Slides* (Video) - Full artifact
• Technical report (Superseded by LICS '18 technical report. Version 2 addresses an erratum concerning the reflection rule, and function extensionality for parametric functions)
• Agda 'parametric' branch (by Andrea Vezzosi)
• Agda proofs and example code
• Put in a more contemporary (2020) perspective in ch. 9 of my PhD thesis.

• Application: Reasoning about Effect Parametricity using Dependent Types (TyDe '19): Extended abstract
  By Joris Ceulemans, Andreas Nuyts, Dominique Devriese

• Thesis - Errata
• This thesis investigates higher directed type theory from a syntactic point of view. The approach is very non-formal, departing not from the question "What can we justify semantically?" but "What syntax rules can we intuitively expect?" Consider it an inventory of non-formal ideas.

Effects in Dependent Type Theory

• Paper

Categorical Secure Compilation

Abstract Congruence Criteria for Weak Bisimilarity (MFCS '21)
By Stelios Tsampas, Christian Williams, Andreas Nuyts, Dominique Devriese, Frank Piessens

• DOI

A Categorical Approach to Secure Compilation (CMCS '20)
By Stelios Tsampas, Andreas Nuyts, Dominique Devriese, Frank Piessens

• DOI - ArXiv

A Summary on Categorical Contextual Reasoning (ACT '19)
By Stelios Tsampas, Andreas Nuyts, Dominique Devriese, Frank Piessens

• Abstract