From dilsat.yuksel at strath.ac.uk Thu Feb 6 15:13:14 2025 From: dilsat.yuksel at strath.ac.uk (Dilsat Yuksel) Date: Thu, 6 Feb 2025 15:13:14 +0000 Subject: [msp-interest] [MSP101] Ezra Schoen: Coequations via proof systems (LT209, 3pm Mon 10-Feb) Message-ID: Hi, On Monday, the MSP101 talk will be given by Ezra Schoen (MSP). See the details of the talk below. Best, Dilsat ********************************************************************** Date: Monday, 10 February at 15:00 Room: LT209, Livingstone Tower Zoom link: https://strath.zoom.us/j/85449272187?pwd=0qNkQqybiaKgBpbEBRv38x11x4db5n.1 Speaker: Ezra Schoen Title: Coequations via proof systems Abstract: What even is a coequation? While Universal Algebra enjoys a set-in-stone consensus on both the correct syntax of equations, as well as what an equation even is, Universal Coalgebra is in no such position. There are many attempts at definitions and syntaxes of coequations, but it is hard to say which one is 'the correct one'. Rather than sorting out this mess, why not add yet another proposal? If we squint, we can see proof systems for modal logic as coequations. This then leads to some fun, natural questions. Which coequations can be captured by what kind of proof systems? If we restrict our attention to a class of 'simple' systems, can we specify "every" coequation? As this is work in progress, I have a fewer answers than questions. The aim of this talk is to introduce coequations in all their colours, and to get the audience to a point where the questions may be appreciated. ********************************************************************** -------------- next part -------------- An HTML attachment was scrubbed... URL: http://lists.strath.ac.uk/archives/msp-interest/attachments/20250206/7fc75c8e/attachment.html From dilsat.yuksel at strath.ac.uk Thu Feb 13 20:46:15 2025 From: dilsat.yuksel at strath.ac.uk (Dilsat Yuksel) Date: Thu, 13 Feb 2025 20:46:15 +0000 Subject: [msp-interest] [MSP101] Clovis Eberhart: Weakest Precondition of Open Coalgebras (LT1414a, 3pm Mon 17-Feb) Message-ID: Hi, On Monday, the MSP101 talk will be given by Clovis Eberhart (MSP). See the details of the talk below. Best, Dilsat ********************************************************************** Date: Monday, 17 February at 15:00 Room: LT1414a, Livingstone Tower Zoom link: https://strath.zoom.us/j/85449272187?pwd=0qNkQqybiaKgBpbEBRv38x11x4db5n.1 Speaker: Clovis Eberhart Title: Weakest Precondition of Open Coalgebras Abstract: Coalgebras are a categorical framework that have proved useful to describe and reason about different types of systems. We define open coalgebras, a compositional framework where coalgebras can be composed as string diagrams. We give them a semantics in terms of weakest precondition predicate transformers computed as a fixed point and link it to previous work on weakest precondition predicate transformers by Aguirre, Katsumara, and Kura. We give several examples of verification problems this semantics can compute, showing its practical usefulness. We give conditions under which this semantics is compositional for the string diagram structure of open coalgebras. Finally, we give a syntactic precomputation of open coalgebras that removes their internal states while preserving their semantics. ********************************************************************** -------------- next part -------------- An HTML attachment was scrubbed... URL: http://lists.strath.ac.uk/archives/msp-interest/attachments/20250213/3ad489a9/attachment.html From dilsat.yuksel at strath.ac.uk Thu Feb 20 09:44:41 2025 From: dilsat.yuksel at strath.ac.uk (Dilsat Yuksel) Date: Thu, 20 Feb 2025 09:44:41 +0000 Subject: [msp-interest] [MSP101] Robert Atkey: Semantic proofs of Cut-elimination for Deep Infererence (LT412, 3pm Mon 24-Feb) Message-ID: Hello, On Monday, the MSP101 talk will be given by Robert Atkey (MSP). See the details of the talk below. Best, Dilsat ********************************************************************** Date: Monday, 24 February at 15:00 Room: LT412, Livingstone Tower Zoom link: https://strath.zoom.us/j/85449272187?pwd=0qNkQqybiaKgBpbEBRv38x11x4db5n.1 Speaker: Robert Atkey Title: Semantic proofs of Cut-elimination for Deep Infererence Abstract: Deep Inference systems are a kind of proof calculus that allow inference rules to be applied anywhere in a formula. Cut-elimination for these systems is similar to that for Sequent calculi: rules that introduce intermediate formulas can be removed from proofs. Prior proofs of cut-elimination relied on intricate syntactic method. I'll talk about a semantic approach that builds a model of the whole calculus from cut-free proofs, such that every proof constructed in this model can be read back as a cut-free proof. This is a similar technique to the one used in Normalisation by Evaluation (NbE). The technique is very flexible and extends to many extensions of Multiplicative Linear Logic, including BV's self-dual non-commutative before connective, additives, and exponentials. This is joint work with Wen Kokke and was published at MFPS last year: https://bentnib.org/sem-cut-elim-mfps.html ********************************************************************** -------------- next part -------------- An HTML attachment was scrubbed... URL: http://lists.strath.ac.uk/archives/msp-interest/attachments/20250220/37a5b2ed/attachment.html From dilsat.yuksel at strath.ac.uk Thu Feb 27 12:10:40 2025 From: dilsat.yuksel at strath.ac.uk (Dilsat Yuksel) Date: Thu, 27 Feb 2025 12:10:40 +0000 Subject: [msp-interest] [MSP101] Fredrik Nordvall Forsberg: Representing type theory in type theory (LT412, 3pm Mon 3-Mar) Message-ID: Hi, On Monday, the MSP101 talk will be given by Fredrik Nordvall Forsberg (MSP). See the details of the talk below. Best, Dilsat ********************************************************************** Date: Monday, 3 March at 15:00 Room: LT412, Livingstone Tower Zoom link: https://strath.zoom.us/j/85449272187?pwd=0qNkQqybiaKgBpbEBRv38x11x4db5n.1 Live stream on Youtube: https://www.youtube.com/@msp101strathclyde4 Speaker: Fredrik Nordvall Forsberg Title: Representing type theory in type theory Abstract: It is often claimed that type theory can act as a foundation of mathematics. If that is so, then type theory should in particular be able to reason about type theory itself. Of course, Dr G?del points out that this cannot work, in general, but we would expect that type theory could still reason about a slightly weaker version of itself. This turns out to be true, but messy, because type theory is quite complicated as a theory. After heroic attempts by Danielsson (2006) and Chapman (2009) to represent type theory internally in type theory, Altenkirch and Kaposi (2016) made a breakthrough in using so-called quotient inductive-inductive types to represent the well typed terms of type theory, where quotient constructors are used to encode beta and eta laws as equalities in the type. Being able to treat such laws as actual equalities is a major improvement, but quickly leads into so-called transport hell, where explicit transports along equalities show up in terms and needs to be reasoned about. I will report on some recent work together with Liang-Ting Chen and Tzu-Chun Tsai on how one can use experimental (and hopefully future) features of Agda to improve on the quotient inductive-inductive representation and remove most uses of transport. ********************************************************************** -------------- next part -------------- An HTML attachment was scrubbed... URL: http://lists.strath.ac.uk/archives/msp-interest/attachments/20250227/dbfc407b/attachment.html