| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Outline of Final Research Achievements |
This study aimed at developing novel semantics of low-level implementations of programming languages via geometric and topological approaches. In particular, we introduced a braided lambda calculus in which permutations of variables are realized by braids carrying information on the low-level geometric implementation. We established the fundamental correspondence between the braided combinatory algebras and braided closed operads, and more generally the correspondence between planar combinatory algebras and planar closed operads, where the construction of operads from combinatory algebras plays the central role. We also investigated new constructions of traced monoidal categories, which give a categorical foundation of our approach, by studying Hopf monads which lift the trace.
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