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arXiv:1701.01285cs.LO

Cofree coalgebras and differential linear logic

James Clift, Daniel Murfet

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Abstract

We prove that the semantics of intuitionistic linear logic in vector spaces which uses cofree coalgebras is also a model of differential linear logic, and that the Cartesian closed category of cofree coalgebras is a model of the simply-typed differential lambda calculus.

arXiv comments
New introduction to the cofree coalgebra and relevant geometric intuition, and a discussion of the differential lambda calculus
Journal reference
Math. Struct. Comp. Sci. 30 (2020) 416-457
DOI
doi:10.1017/S0960129520000134
Subjects
cs.LOLogic in Computer Science

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Discussed in comments1 thread

  1. Linear logic and deep learning [pdf] 1 comment

    • Author here. The theoretical background can be found in: https://arxiv.org/abs/1407.2650 https://arxiv.org/abs/1701.01285 http://therisingsea.org/notes/MScThesisJamesClift.pdf As neel_k notes, a good way to understand this picture is in terms of differential linear logic (a…

      dmurfetView on HNParent context

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