For a new seminar on the proofs and algorithms pole of LIX, we are happy to welcome Bryce Clarke (LIX), invited by the PARTOUT team.

Details for joining the online conference:

• Link: https://us02web.zoom.us/j/89155612228?pwd=aU5RYXAvYXpvbmFROG44OVpUVkxSZz09
• Meeting ID: 891 5561 2228
• Passcode: ZLEY8Z Clarke (LIX), invited by the PARTOUT team.

Abstract: Bidirectional transformations are a means of maintaining consistency between a pair of systems. In 2005, the mathematical structure of a lens was introduced to model bidirectional transformations, and has since grown into an active topic of research in computer science and applied category theory. Classically, a system may be modelled by its set of possible states, leading to a particular notion of lens, however as more sophisticated models of systems have developed, more interesting and useful notions of lens have arisen.

The aim of this talk is to investigate lenses between preordered sets. The principal idea is that a system is modelled by its set of states equipped with a preorder, which specifies when one state may transition to another, while a lens is an order-preserving function with certain additional structure. Throughout the talk we will explore answers to several natural questions regarding the mathematical structure of lenses. How do lenses compose and decompose, both sequentially and in parallel? What are the ways in which we can build new lenses with nice properties? Given an order-preserving function, how many lens structures does it admit, and is it possible to freely generate a lens structure from it? The talk will focus on demonstrating answers to these questions via small “toy” examples, and aims to be accessible without prior knowledge of category theory. If time allows, I will discuss how the framework of lenses may be extended when systems are instead modelled by generalised metric spaces or weighted categories.

The list of next seminars can be found at: https://www.lix.polytechnique.fr/proofs-algorithms/seminar/

The calendar of seminars can be found at: https://www.lix.polytechnique.fr/proofs-algorithms/seminar/calendar.ics