ICE-TCS: Sergey Goncharov, Friedrich-Alexander-Universität Erlangen-Nürnberg

Guarded traced categories for recursion and iteration

  • 2.4.2019, 12:10 - 13:00

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ICE-TCS seminar #331

Date and time: Tuesday, 2 April 2019, 12:10-13:00
Location: Room M120
Speaker: Sergey Goncharov, Friedrich-Alexander-Universität Erlangen-Nürnberg WWW: https://www8.cs.fau.de/sergey

Title: Guarded traced categories for recursion and iteration

Abstract: Abstract guardedness is a unifying mechanism allowing for the identification of the equational theory of partial trace operators in (symmetric) monoidal categories in a compositional way. Examples include classical total iteration and recursion, partial recursion in categories of pre-domains and complete metric spaces, partial iteration in categories for modeling concurrent processes and hybrid programs, as well as traces in infinite-dimensional Hilbert spaces. In my talk I will concentrate on (uniform) guarded trace operators in co-Cartesian and Cartesian categories, in particular, those ones that are generated by monads and comonads. I will present recent results on axiomatizing the theory of guarded fixpoints with applications to process algebra in monad-based form where the notion of guardedness originated. 

This is a joint work (in progress) with Lutz Schröder and Paul Levy.