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Applied Mathematics Lab (Masahito Hasegawa)
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A lab that uses category theory to uncover the mathematical structures underlying computation.
AboutAbout the lab
Extracting and analyzing the mathematical structure of computation.
The Hasegawa Lab studies theoretical computer science, particularly the semantics of programming languages.
The lab aims to extract and analyze the mathematical structures underlying computation, so that the wide variety of software on computers can be discussed in a unified and rigorous way.
The approach is to understand complex computational phenomena through appropriately abstracted structures; in a sense, it is a "representation theory of computation."
The lab mainly uses algebraic and category-theoretic methods, together with the frameworks of proof theory and type theory.
Key terms
- Semantics
- A theory that rigorously expresses what a program computes as a mathematical object.
- Category theory
- A theory that treats mathematical structures by focusing on objects and on how the arrows (morphisms) between them connect.
- Monad
- A structure for handling things such as computations with side effects in a unified way, in the language of category theory.
ResearchResearch themes
The lab's research aims to extract and analyze the mathematical structures underlying computation. It analyzes and applies mathematical models of programming languages (semantics) using algebraic and category-theoretic methods and frameworks from proof theory and type theory.
*Illustrative imageRepresentation theory of computation
To discuss a wide variety of software in a unified and rigorous way, the lab identifies appropriately abstracted structures that represent complex computational phenomena, and seeks to gain useful insights into those phenomena by studying these structures.
*Illustrative imageModels of recursion, side effects, and linear logic
The lab has studied monad-based models of computation with side effects, as well as type theories based on linear logic and their models in monoidal categories.
*Illustrative imageProgram semantics and quantum topology
The lab explores the connections between program semantics and quantum topology and quantum computation.
MembersFaculty
- ProfessorMasahito Hasegawa
VoicesStudent voices
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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: “Kleisli Category - morphism composition” AugPi / CC BY-SA 4.0 (cropped)
- Representation theory of computation: “CommutativeClifford” AromaticPolygon / CC0 (cropped)
- Models of recursion, side effects, and linear logic: “Commutative diagram used in proof of relative exact sequence” Dom walden / CC BY-SA 4.0 (cropped)
- Program semantics and quantum topology: “Quantum gate teleportation” Vtomole / 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 (Applied Mathematics Division (Kobayashi) Lab): “Graph-matroid” Didia / CC BY-SA 4.0 (cropped)
- Related lab (Applied Mathematics Division (Kawakita) Lab): “Du Val singularities” Aizenr / CC BY-SA 4.0 (cropped)
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