FERNANDO LUCATELLI NUNES

Ph.D. in Computer Science

Freely Generated Categorical Structures and Automatic Differentiation

Utrecht University, Department of Information and Computing Sciences. Thesis submitted; degree to be awarded in 2026.

• Period November 2020 – November 2025
• Supervisors Professor Gabriele Keller and Dr. Matthijs Vákár.
• Committee Ieke Moerdijk, Bart Jacobs, Sam Staton, Robin Cockett, and Patricia Johann.

Main themes

Programming language semantics; categorical semantics; automatic differentiation; CHAD; dual-numbers automatic differentiation; logical relations; program transformations; recursion and iteration; type systems; dependent types; algebraic effects; Grothendieck constructions.

Publications related to the Ph.D.

• Monoidal closure of Grothendieck constructions via Σ-tractable monoidal structures and Dialectica formulas Lucatelli Nunes, F.; Vákár, M. Theory and Applications of Categories, 44, 1153–1217, 2025. 65 pages. (arXiv)
• Free extensivity via distributivity Lucatelli Nunes, F.; Prezado, R.; Vákár, M. Portugaliae Mathematica, 82(1–2), 177–204, 2025. 28 pages. (DOI; arXiv)
• Unraveling the iterative CHAD Lucatelli Nunes, F.; Plotkin, G.; Vákár, M. Accepted for publication in Mathematical Structures in Computer Science. arXiv:2505.15002, 2025, 57 pages.
• Free doubly-infinitary distributive categories are cartesian closed Lucatelli Nunes, F.; Vákár, M. Accepted for publication in Applied Categorical Structures. arXiv:2403.10447, 2024, 16 pages.
• Automatic differentiation for ML-family languages: correctness via logical relations Lucatelli Nunes, F.; Vákár, M. Mathematical Structures in Computer Science, 34(8), 747–806, 2024. 60 pages. (DOI; arXiv)
• Homomorphic reverse differentiation of iteration Lucatelli Nunes, F.; Plotkin, G.; Vákár, M. LAFI 2024, Tenth Workshop on Languages for Inference at POPL, 2024. 2 pages.
• CHAD for expressive total languages Lucatelli Nunes, F.; Vákár, M. Mathematical Structures in Computer Science, 33(4–5), 311–426, 2023. 116 pages. (DOI; arXiv)
• Logical relations for partial features and automatic differentiation correctness Lucatelli Nunes, F.; Vákár, M. Oberwolfach Preprints, OWP-2023-09, 2023. arXiv:2210.08530, 2022, 21 pages.

The publications listed above arose from my Ph.D. work in Computer Science.