## Abhishek Kr Singh

I am a research scholar in the School of Technology and Computer Science at TIFR Mumbai, since Aug 2012. I did my M.Tech. in Media and Sound Engineering from IIT Kharagpur and B.Tech. in CSE from Govt. College of Engineering and Textile Technology Berhampore. At TIFR, I am working with Prof. N Raja (superviser).

## Contact

Office: A 222

STCS, TIFR, Homi bhaba road,

Colaba, 400005 Mumbai, India.

Email: abhishek.singh@tifr.res.in

Phone: +91 22 2278 2338

## Research interests

I am broadly interested in the study of Computability Theory. My current research interest is in the formalization of mathematics using theorem provers. In particular, I am trying to use the Coq proof assistant to formalize some interesting results from Combinatorics.

## Projects

I did a reading project titledInteractive theorem proving in Coq and the Curry-Howard Isomorphismunder the guidance of Prof. N Raja. Aim of the project was to study the relationship between logic and type theory and how this relationship helps in realizing Proof Assistants like Coq. My project report summarises the study and explains very briefly the theoretical foundations of the Coq Proof Assistant.## Coq Codes

- Dilworth and Dual-Dilworth in Coq [zip].
- Dilworth's, Hall's and Erdos-Szekeres theorems in Coq [zip].
## Research Articles

- A. K. Singh, "Interactive theorem proving in Coq and the Curry-Howard Isomorphism", Reading Project Report, TIFR Mumbai (2015).
- A. K. Singh and N. Raja, "Separation Logic to Meliorate Software Testing and Validation", Trends in Software Testing, Springer-Verlag (2016), pp 89-109 [arxiv].
- A. K. Singh, "Fully Mechanized Proofs of Dilworth's Theorem and Mirsky's Theorem ", Indian Conference on Logic and its Applications (ICLA-17)[arxiv].
- A. K. Singh, "Formalization of some central theorems in combinatorics of finite sets" IWIL Workshop and LPAR-21 Short Presentation Papers [arxiv].
## Presentations

- Surreal Numbers, Student Seminar, TIFR Mumbai (Oct 4, 2013).
- An introduction to Recursive Function Theory, TIFR Mumbai (2014) [part1 part2].
- Interactive theorem proving in Coq and the Curry-Howard Isomorphism, Project Seminar, TIFR Mumbai (Feb 20, 2015) [slides].
- The Perfect Graph Theorem, Student Seminar, TIFR Mumbai (Jan 13, 2017).
- Formalization of some central theorems in combinatorics of finite sets, LPAR-21, Botswana (May 9, 2017) [slides].