I have joined Amazon Web Services as an applied scientist in November 2024!

I almost(!, defence-only) obtain my PhD from McGill University, under the supervision of Professor Brigitte Pientka. I did my Master of Mathematics at the University of Waterloo, supervised by Professor Ondřej Lhoták. Before that, I worked in the industry since 2014. My undergrad was at Fudan University.

These days, I am mainly working on programming languages and formal proofs using proof assistants based on Martin-Löf type theory, e.g. Coq and Agda. I am particularly interested in various type theories and the mathematics behind them. As a purist, I insist that if a proof can be done constructively, then it needs to be; if a mechanized proof can be established, there is no reason not to.

Before heading back to school, I worked as an engineer on a number of projects involving performance engineering, configurations, and others that you might expect to see in the industry. Back in my old days at Fudan University, I was more of a robotic guy.

I am awarded the Postgraduate Scholarship-Doctoral by the Natural Sciences and Engineering Research Council of Canada.

I am in support of 996.icu activity .

Doctor of Philosophy

Computer Science

Grade: 4.0/4.0

Thesis:
**Foundations and Applications of Modal Type Theories**
(code)

A series of studies of modal type theories in different styles, with applications in meta-programming

Abstract

Over the past few decades, type theories as mathematical foundations have been extensively studied and are well understood. Many proof assistants implement type theories and have found important applications to provide critical security guarantees. In these applications, users often write meta-programs, programs that generate other programs, to implement proof search heuristics and improve their work efficiency. However, as opposed to the deep understanding of type theories, it remains unclear what foundation is suitable to support meta-programming in proof assistants. In this thesis, I investigate modal type theories, a specific approach to this problem. In modal type theories, modalities are a way to shallowly embed syntax into the systems, so users can write meta-programs that manipulate syntax through these modalities.

I explore two different styles of modal systems. In the first part, I investigate the Kripke-style systems, which faithfully model the familiar quasi-quoting style of meta-programming. I develop an explicit substitution calculus and scale it to dependent types, introducing Mint. I prove strong normalization of Mint, which implies its logical consistency, using an untyped domain model.

Nevertheless, the Kripke-style systems only support composition and execution of code, and they cannot easily support a general recursion principle on the structure of code. To support such a general recursion principle, I develop the layered style, where a system is divided into nested layers of sub-languages. The layered style scales quite naturally to dependent types, introducing DeLaM. DeLaM allows users to compose, execute and recurse on dependently typed code. I prove that DeLaM is weakly normalizing and its convertibility problem between types and terms is decidable. Hence, DeLaM provides a type-theoretic foundation to support type-safe meta-programming in proof assistants.

Courses:

- COMP 550 Natural Language Processing (report)
- COMP 520 Compiler Design (report) (code)
- COMP 596 Topics in Computer Science 3 (Theoretical Foundations of Reliable Meta-programming) (report)
- COMP 700 Comprehensive Examination (report)
- IFT 6172 Semantics of programming languages (at University of Montreal) (report) (code)
- COMP 701 Thesis Proposal and Area Examination (report) (slides)

09 / 2019 - present

Master of Mathematics

Computer Science

Grade: 94.4/100

Thesis: Decidability and Algorithmic Analysis of Dependent Object Types (DOT) (code) (slides)

Investigation on (un)decidability and algorithmic properties of the family of DOT calculi

Abstract

Dependent Object Types, or DOT, is a family of calculi developed to study the Scala programming language. These calculi have path dependent types as a feature, and potentially intersection types, union types and recursive types. So far, the study of DOT calculi mostly focuses on the soundness proof, which does not directly contribute to development of compilers. This thesis presents a detailed investigation of decidability and algorithmic properties of the family of DOT calculi.

In decidability analysis, the undecidability of subtyping of several calculi is formally established, including the D<: and D∧ calculi. Prior to this investigation, the undecidability of subtyping of all DOT calculi including D<: was open. Decidability analysis puts emphasis on a particular form of subtyping rules, called normal form. It turns out that a normal form definition is not only as expressive, but also more suggestive than the original definition. A conceptual device, called small-step analysis, is introduced to assist converting a usual definition of subtyping to its normal form definition. Moreover, decidability analysis gives direct contributions to the algorithmic analysis, by revealing two decidable fragments of D<: in declarative form, called the kernels. Decidability analysis also suggests a novel subtyping algorithm framework, stare-at subtyping. Stare-at subtyping and an existing algorithm are shown to be sound and complete w.r.t. their corresponding kernels.

In algorithmic analysis, stare-at subtyping is extended to other calculi, with more features than D<:, including D∧, μDART and jDOT. In μDART and jDOT, bi-directional type assignment algorithms are developed. The algorithms developed in this thesis are all shown to be sound with respect to their target calculi and terminating.

During the development of the algorithms, analysis shows a number of ways in which the Wadlerfest DOT calculus does not directly correspond to the Scala language, while substantially increases the difficulties of algorithmic design. jDOT, therefore, is developed as an alternative formalization of Scala.

09 / 2017 - 08 / 2019

Bachelor of Science

Electronic Engineering

Grade: 3.35/4.0

09 / 2010 - 07 / 2014

Jason Hu and Brigitte Pientka

2024

Jason Hu, Junyoung Jang, Brigitte Pientka

2023

Jason Hu and Brigitte Pientka

2022

Jason Hu, Brigitte Pientka, Ulrich Schöpp

2022

2021

Jason Hu and Ondřej Lhoták

2020

Jason Hu and Brigitte Pientka

2024

2023

Jason Hu and Brigitte Pientka

2022

2021

Teaching Assistant

COMP 360, Algorithm Design

COMP 302, Programming Languages and Paradigms

COMP 527, Logic and Computation

COMP 523, Language-based Security

09 / 2019 - present

Teaching Assistant / Instructional Apprendice

CS 241, Foundation of Sequentual Programs

CS 343, Concurrent and Parallel Programming

09 / 2017 - 08 / 2019

fall 2022

summer 2021

2021

summer 2020

01/19/2020-01/25/2020

with fellowship

2019

with fellowship

2018

Applied Scientist II

11 / 2024 - present

Applied Scientist Intern

05 / 2023 - 08 / 2023

Applied Scientist Intern

06 / 2022 - 09 / 2022

Applied Scientist Intern

05 / 2020 - 08 / 2020

Summer Analyst Intern

05 / 2018 - 08 / 2018

Java / Scala Developer

10 / 2015 - 07 / 2017

Software Developer

08 / 2014 - 10 / 2015

.Net Engineer Intern

05 / 2014 - 06 / 2014

QA Intern

07 / 2013 - 08 / 2013

09 / 2020 - 08 / 2023

09 / 2020 - 08 / 2024

09 / 2020 - 08 / 2022

01 / 2020 - 04 / 2020

I speak four languages: English, Mandarin, Cantonese and Japanese.

I am actively learning French at McGill now!

I had 6 years of math, 2 years of physics and 1 year of chemistry olympiads experience.

I am a Cantonese. My town is Foshan. Warning: I've got no idea how to perform Wing Chun.

I like superheroes, Marvel, DC and whatever you can name.

I played a lot of badminton during my undergrad, and now I resume to play again in Badminton Montreal!

I have lots of video games in my Steam library, and I dream to have time to play!