# Logic Seminar - Nicola Gambino (Manchester)

Dates: | 5 October 2022 |
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Times: | 15:15 - 16:15 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Title: Differential lambda-calculus and analytic functors

Abstract: In a seminal 2003 paper, Ehrhard and Regnier introduced the differential lambda-calculus, an extension of the lambda-calculus with a differential operator. Among other things, the differential lambda-calculus leads to the possibility of approximating lambda-terms by a form of the Taylor series expansion. This seminar will present a model of the typed differential lambda-calculus. The model is built using a generalisation of Joyal's analytic functors, which are a functorial counterpart of exponential power series. Its core is a cartesian closed 2-category which can be understood as a `categorified' version of the relational model of Linear Logic. The material is based on collaborative work with M. Fiore, M. Hyland, A. Joyal and G. Winskel.