LAB LOGA page on LabLog, a review site (not the lab's official page)
Terui Lab
Machine-translated · View original
A lab that studies proofs themselves from both mathematical and computational perspectives.
AboutAbout the lab
Proofs, from both mathematics and computation
The Terui Lab studies proofs themselves from the standpoint of mathematical logic.
A proof is a means of doing mathematics, but it can also be an object of mathematics: when represented appropriately, the mathematical structure behind it comes into view.
Under the Curry–Howard correspondence, a proof can be regarded as (to a certain extent) the same thing as a functional program, so it also has an aspect as a "medium of computation."
The lab approaches the subject from various perspectives, including computational complexity, games, denotational semantics, and algebraic semantics.
Key terms
- Curry–Howard correspondence
- A relationship in which proofs in logic and computer programs correspond to each other.
- Computational complexity
- The idea of measuring how difficult a problem is by the amount of time or memory needed to solve it.
- Lambda calculus
- A foundational system in the theory of programs that expresses computation using only the construction of functions and the application of functions to values.
ResearchResearch themes
Under the title "Mathematical Science of Proofs," the lab studies proofs from multiple perspectives, including computational complexity, games, denotational semantics, and algebraic semantics. In recent years, it has been exploring whether insights from mathematical logic and the foundations of programming languages can be applied to research on methods for discovering proofs.
*Illustrative imageAlgebraic proof theory for non-classical logics
The lab proposed algebraic proof theory for non-classical logics and investigated the correspondence between ordered algebras and proof theory. The main aim is to make techniques from ordered algebra and proof theory usable in both directions.
*Illustrative imageComputational complexity of the simply typed lambda calculus
The lab precisely characterized the computational complexity of the simply typed lambda calculus (intuitionistic propositional logic).
*Illustrative imageAlgebraization of the Ω-rule
The lab incorporated the Ω-rule, one of the key techniques of traditional proof theory (ordinal analysis), into the contexts of lambda calculus and structural proof theory, and gave it an algebraic interpretation.
MembersFaculty
- Associate ProfessorKazushige Terui
VoicesStudent voices
Ratings and reviews reflect the experiences of individual current or former students, not the lab's official views. Whether a lab has reviews, or how many, says nothing about the lab itself.
Students who take part in an interview may receive a thank-you gift worth ¥1,000, regardless of what they say.
Student ratings (0 students)
--
--
--
--
--
--
Student voices answer questions like these
- What's great about this lab?
- What did you learn after joining?
- What's the vibe, and what is the professor like?
- Who is this lab for?
- Where do graduates go?
Your experience can help younger students choose their lab. Your name won't be shown.
Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Terui Lab
Applied Mathematics Lab (Masahito Hasegawa)Research Institute for Mathematical Sciences, Division of Applied Mathematical SciencesComputer science / theoretical computer science, software sc…
Applied Mathematics Division (Kawamura) LabResearch Institute for Mathematical Sciences, Division of Applied Mathematical SciencesComputer science / theory of computation (computability and …
Applied Mathematics Lab (Kazuhisa Makino)Research Institute for Mathematical Sciences, Division of Applied Mathematical SciencesApplied mathematics and computational science / discrete mat…
Kuwagaki LabResearch Institute for Mathematical SciencesGeometry / differential geometry, algebraic analysis, mathem…The information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Hasse4Conn” R. J. Mathar / CC BY-SA 4.0 (cropped)
- Algebraic proof theory for non-classical logics: “Hasse Diagram of Subgroup Lattice of D4” Spamakin / CC0 (cropped)
- Computational complexity of the simply typed lambda calculus: “A lambda-term with links” PIerre.Lescanne / CC BY-SA 4.0 (cropped)
- Algebraization of the Ω-rule: “Gerhard Gentzen” Eckart Menzler-Trott / CC BY-SA 2.0 de (cropped)
- Related lab (Applied Mathematics Lab (Masahito Hasegawa)): “Kleisli Category - morphism composition” AugPi / CC BY-SA 4.0 (cropped)
- Related lab (Applied Mathematics Division (Kawamura) Lab): “Turing Machine” Porao / Public domain (cropped)
- Related lab (Applied Mathematics Lab (Kazuhisa Makino)): “B functies 2var versie02” Bob.v.R / CC BY-SA 4.0 (cropped)
- Related lab (Kuwagaki Lab): “Whitney umbrella” Jlrodri / CC BY-SA 3.0 (cropped)
About LabLog
LabLog is a lab review app for students only. Student members at each university interview students in labs and publish what they say. Student voices can only be read by students who sign up with a university email address. Operated by bestiee Inc.
Learn more about LabLog ↗Search engines and AI may reference the basic lab info and rating summaries on this page and the description of LabLog. Student voices are for student members only. Automated collection by programs (scraping, or input to or training of AI) is prohibited under Article 8 of the Terms of Service. If you need data for research or analysis, please contact us.