2026-08-17T12:00:59Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:5969 2024-03-06T10:37:23Z ddc:004 open_access

Coalgebras and Higher-Order Computation: a GoI Approach Hasuo, Ichiro functional programming geometry of interaction categorical semantics coalgebra Girard's geometry of interaction (GoI) can be seen---in one practical aspect of it---as a compositional compilation method from functional programs to sequential machines. There tokens move around and express interactions between (parts of) programs. Intrigued by the combination of abstract structures and concrete dynamics in GoI, our line of work has aimed at exploiting, in GoI, results from the theory of coalgebra---a categorical abstraction of state-based transition systems that has found its use principally in concurrency theory. Such reinforced connection between higher-order computation and state-based dynamics is made possible thanks to an elegant categorical axiomatization of GoI by Abramsky, Haghverdi and Scott, where traced monoidal categories are identified to be the essential structure behind. In the talk I shall lay out these basic ideas, together with some of our results on: GoI semantics for a quantum programming language; and our ``memoryful'' extension of GoI with algebraic effects. The talk is based on my joint work with my colleague Naohiko Hoshino (RIMS, Kyoto Univer- sity) and my (former) students Koko Muroya (University of Birmingham) and Toshiki Kataoka (University of Tokyo), to whom I owe special thanks. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ichiro Hasuo 2016 Is Part Of LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2016.2 urn:nbn:de:0030-drops-59698 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.2 eng https://creativecommons.org/licenses/by/3.0/legalcode