Evan Cavallo


I'm a postdoctoral fellow in the Computational Mathematics division at Stockholm University, hosted by Anders Mörtberg. Previously, 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 asconstructions. My current research focuses on the constructive reading of equality proofs as paths in a space, which is the basis of cubical type theories. I am developing features we can build into these theories (such as higher inductive types and internal parametricity), exploring their applications (such as for representation independence), and working to systematize the design of cubical type theories.

Address mail to evan.cavallo, postal code math.su.se.


Publications


22.05 | Modalities and parametric adjoints.
Daniel Gratzer, Evan Cavallo, G.A. Kavvos, Adrien Guatto, & Lars Birkedal.
Transactions on Computational Logic.
[Paper]
21.11 | Internal parametricity for cubical type theory.
Evan Cavallo & Robert Harper.
Logical Methods in Computer Science.
Extended version of CSL 2020 paper.
[Paper] [arXiv]
21.01 | Internalizing representation independence with univalence.
Carlo Angiuli, Evan Cavallo, Anders Mörtberg, & Max Zeuner.
Principles of Programming Languages (POPL) 2021.
[Paper] [Cubical Agda] (errata)
20.01 | Internal parametricity for cubical type theory.
Evan Cavallo & Robert Harper.
Computer Science Logic (CSL) 2020.
[Paper] [Tech report]
20.01 | Unifying cubical models of univalent type theory.
Evan Cavallo, Anders Mörtberg, & Andrew W Swan.
Computer Science Logic (CSL) 2020.
[Paper] [Tech report: type theory] [Tech report: model structure] [Agda formalization]
19.01 | Higher inductive types in cubical computational type theory.
Evan Cavallo & Robert Harper.
Principles of Programming Languages (POPL) 2019.
[Paper] [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.
[Paper]

Preprints, notes, &c.


22.11 | Relative elegance and cartesian cubes with one connection.
Evan Cavallo and Christian Sattler.
Preprint.
[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.
[Thesis]

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


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 (invited talk). [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] [Note]

Teaching


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


21– | Postdoctoral Fellow in Computational Mathematics @ Stockholm 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.