2023 Fiscal Year Final Research Report
Design and analysis of low-level programming languages via low-dimensional topology
| Project/Area Number |
21K11753
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60010:Theory of informatics-related
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Keywords | プログラミング言語 / 意味論 / 圏論 / 低次元トポロジー / モノイダル圏 / ラムダ計算 / コンビネータ代数 |
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| Outline of Final Research Achievements |
Traditional program semantics has achieved many results on high-level programming languages. On the other hand, semantics on the low-level implementation model of programming languages is still in the developing stage. This research focuses on the affinity between low-level implementation models and low-dimensional topology such as knot theory, and aims to construct topological program semantics that can support low-level implementation models. As first steps towards this direction, we introduced a theory of planar combinatory algebras in terms of operads and monoidal categories, and studied a braided lambda calculus in which swapping of variables are realized by braids. Furthermore, we introduced ribbon combinatory algebras, which correspond to ribbon categories used in the study of invariants of knots and tangles. At the same time, we studied traced monoidal categories and their lifting problem via Hopf monads.
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| Free Research Field |
理論計算機科学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究はプログラミング言語の理論の基礎付けに関するものであり、圏論や幾何学・トポロジーの知見や技法をプログラム意味論に取り入れること、および必要となる圏論の整備の両方を目指したものである。本研究によりプログラミング言語設計やプログラム検証に用いることのできる数学的手法が拡充され、短期的には、このような低次元トポロジー的なアプローチに基づく理論研究の活性化・深化、また、長期的には、実装レベルに踏み込んだソフトウェア開発・検証技術の発展に寄与することが期待される
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