Evan Cavallo

I am a postdoc in the Logic and Types group at Göteborgs universitet under Thierry Coquand. Previously I was a postdoc in the Computational Mathematics division at Stockholms universitet under Anders Mörtberg, and before that I was a Ph.D. student in computer science at Carnegie Mellon University under Robert Harper.

I study constructive type theories, particularly new ways to treat proofs as constructions. My current research focuses on the constructive reading of proofs of equality as paths in space, which is the basis of cubical type theories. I am developing extensions to these theories (such as higher inductive types and internal parametricity), exploring their applications (such as for representation independence), studying their connections to homotopy theory, and working to systematize their design.

Address mail to evan.cavallo, postal code gu.se.
I am @ecavallo@mathstodon.xyz on Mastodon.

Latest:

Publications

24.05 | Automating boundary filling in Cubical Agda.
Maximilian Doré, Evan Cavallo, & Anders Mörtberg.
Formal Structures for Computation and Deduction (FSCD) 2024.
[DOI] [arXiv]
22.05 | Modalities and parametric adjoints.
Daniel Gratzer, Evan Cavallo, G.A. Kavvos, Adrien Guatto, & Lars Birkedal.
Transactions on Computational Logic (TOCL).
[DOI] [local copy]
21.11 | Internal parametricity for cubical type theory.
Evan Cavallo & Robert Harper.
Logical Methods in Computer Science (LMCS).
Extended version of CSL 2020 paper.
[DOI] [arXiv]
21.01 | Internalizing representation independence with univalence.
Carlo Angiuli, Evan Cavallo, Anders Mörtberg, & Max Zeuner.
Principles of Programming Languages (POPL) 2021.
[DOI] [local copy] [formalization] (errata)
20.01 | Internal parametricity for cubical type theory.
Evan Cavallo & Robert Harper.
Computer Science Logic (CSL) 2020.
[DOI] [local copy] [tech report]
20.01 | Unifying cubical models of univalent type theory.
Evan Cavallo, Anders Mörtberg, & Andrew W Swan.
Computer Science Logic (CSL) 2020.
[DOI] [local copy] [tech report: type theory] [tech report: model structure] [formalization]
19.01 | Higher inductive types in cubical computational type theory.
Evan Cavallo & Robert Harper.
Principles of Programming Languages (POPL) 2019.
[DOI] [local copy] [tech report]
18.07 | The RedPRL proof assistant.
Carlo Angiuli, Evan Cavallo, Favonia, Robert Harper, & Jonathan Sterling.
Logical Frameworks & Meta Languages: Theory & Practice (LFMTP) 2018. Invited paper.
[DOI] [arXiv]

Preprints, notes, &c.

24.06 | The equivariant model structure on cartesian cubical sets.
Steve Awodey, Evan Cavallo, Thierry Coquand, Emily Riehl, & Christian Sattler.
Preprint.
[arXiv] [formalization: HTML interface] [formalization: source]
22.11 | Relative elegance and cartesian cubes with one connection.
Evan Cavallo & Christian Sattler.
Submitted.
[arXiv]
21.02 | Higher inductive types and internal parametricity for cubical type theory.
Evan Cavallo.
Ph.D. thesis in Computer Science @ Carnegie Mellon U.
[CMU technical report]
(revised May 2021: errata)
19.10 | "Stable factorization from a fibred algebraic weak factorization system".
Evan Cavallo.
Unpublished note.
[arXiv]
15.12 | Synthetic cohomology in homotopy type theory.
Evan Cavallo.
Master's thesis in Mathematical Sciences @ Carnegie Mellon U.
[local copy]

Code

agda/cubical [github] – co-maintainer
A library for the --cubical mode of the Agda proof assistant.
ptt [github] – creator
An experimental implementation of a type-checker for a type theory with internal parametricity, using Gratzer, Sterling, and Birkedal's blott as a base.
redtt & RedPRL [website] – contributor
Proof assistants for cartesian cubical type theory.

Selected talks

24.03 | Interpreting cubical types as spaces.
@ Stockholm Logic Seminar [slides]
24.03 | Why some cubical models don't present spaces.
@ HoTT Electronic Seminar Talks [slides] [video]
22.11 | Cubes with one connection and relative elegance.
@ HoTT Electronic Seminar Talks [slides] [video]
21.04 | Fitch-style modalities and parametric adjoints.
@ Stockholm-Göteborg Joint Seminar [slides]
20.01 | Internal parametricity for cubical type theory.
@ CSL 2020 [slides]
20.01 | Unifying cubical models of univalent type theory.
@ CSL 2020 [slides]
19.06 | Cubical indexed inductive types.
@ HoTT-UF 2019 [slides]
19.06 | Internally parametric cubical type theory.
@ TYPES 2019 [slides]
19.03 | Parametric cubical type theory.
@ HoTT Electronic Seminar Talks [slides] [video]
19.01 | Higher inductive types in cubical computational type theory.
@ POPL 2019 [slides] [video]
14.09 | The Mayer-Vietoris sequence and cubes.
@ Oxford HoTT Workshop [slides]

Teaching

24.Sp | TA for DAT280/DIT261 Parallel functional programming
24.Sp | TA for TDA342 Advanced functional programming
23.Sp | Instructor for DA2005 Programming techniques
22.Fa | Instructor for DA2005 Programming techniques
22.Sp | Instructor for DA2005 Programming techniques
16.Fa | TA for 15-317 Constructive Logic
15.Fa | TA for 15-814 Types and Programming Languages
15.Sp | TA for 15-312 Foundations of Programming Languages
14.Fa | TA for 15-317 Constructive Logic

Status

23– | Postdoc in Logic and Types @ Göteborgs U.
21–23 | Postdoc in Computational Mathematics @ Stockholms U.
15–21 | Ph.D. student in Computer Science @ Carnegie Mellon U.
10–15 | Undergraduate & Honors Master's student in Mathematical Sciences @ Carnegie Mellon U.