2026-07-20T12:09:20Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:3238 2024-03-06T10:34:00Z ddc:004 open_access

The Lax Braided Structure of Streaming I/O Jeffrey, Alan Rathke, Julian semantics categorical models streaming I/O Agda We investigate and implement a model of typed streaming I/O. Each type determines a language of traces analogous to regular expressions on strings, and programs are modelled by certain monotone functions on these traces. We show that sequential composition forms a lax braided monoid in the category of types and programs. This lax braided structure allows programs to be represented diagrammatically using Joyal and Street's string diagrams in 3D space. Monotone functions over traces cannot be executed efficiently, so we present an equivalent monoidal category of transducers. We demonstrate that transducers can be executed efficiently, theoretically by showing that programs with diagrams embedded in the plane can be executed in O(1) space, and experimentally by an implementation in the Agda dependently typed functional language. Agda supports machine-assisted proof: we have mechanically verified that the transducer implementation and the I/O model form lax braided monoidal categories. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alan Jeffrey and Julian Rathke 2011 Is Part Of LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2011.292 urn:nbn:de:0030-drops-32386 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.292 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode