JuiHsuan Wu (Ray) 吳睿軒
PhD student  Institut Polytechnique de Paris & Inria Saclay
About
Hi! I am JuiHsuan Wu, a PhD student at LIX, Ecole Polytechnique & Inria Saclay advised by Dale Miller. I also go by the name Ray.
Before, I studied computer science and mathematics at Ecole Normale Supérieure and got a master degree from Master Parisien de Recherche en Informatique. You can have a look at my CV (Version française).
Research topic
I am working on term representations based on proof theory.
Terms (or expressions) are essential in many different settings: mathematical proofs, programming languages, proof assistants and so on. Proof theory has been widely used to motivate the design of term structures via notably the CurryHoward correspondence.
The goal of my PhD project is to build a logical framework based on proof theory to describe/unify/justify different term representations, in the hope that prooftheoretic considerations will on one hand provide careful and formal descriptions of term structures and on the other hand give us more insights on terms.
Instead of using proof systems such as Gentzen’s natural deduction and sequent calculus, we use the focused proof system LJF in order to give more structure to proofs. The notion of polarization gives the flexibility to construct differents forms of proofs, which is a desirable feature since we want to describe different term structures in our system.
I am also working on graphical representations for terms related to the term structures obtained as described above.
Some problems I am thinking about:

How can terms (proofs) built using different polarization interact with each other?

How can terms (proofs) built using different axioms interact with each other?

What is the “meaning” of a term from a purely logical point of view?
Misc
Find out how my name is pronouced: Jui, 睿 (sounds like ray in English) and Hsuan, 軒.
APLL, an automated prover for linear logic designed and implemented by me.
I am a music enthusiast. I mainly listen to Hip Hop, R&B and Jazz. My favorite artists are Soft Lipa, Loyle Carner, FKJ, Mac Miller, H.E.R., Nick Hakim, …
My brother is a freelance illustrator, check out his works here.
News
Aug 1, 2022  I gave the talk “A positive perspective on term representation: work in progress” at LFMTP 2022, Haifa, Israel. Slides. 

Jun 27, 2022  I gave the talk “A positive perspective on term representation” at Proofs and Algorithms seminar, LIX/Inria Saclay (online). Slides. 
Oct 1, 2021  I joined the PARTOUT team at Inria Saclay as a PhD student. 
Publications & preprints

CSL 2023

LFMTP 2022

LICS 2021Combinatorial Proofs and Decomposition Theorems for Firstorder LogicIn 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2021