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Title: A Nominal Approach to Probabilistic Separation Logic
Currently, there is a gap between the tools used by probability theorists and those used in formal reasoning about probabilistic programs. On the one hand, a probability theorist decomposes probabilistic state along the simple and natural product of probability spaces. On the other hand, recently developed probabilistic separation logics decompose state via relatively unfamiliar measure-theoretic constructions for computing unions of sigma-algebras and probability measures. We bridge the gap between these two perspectives by showing that these two methods of decomposition are equivalent up to a suitable equivalence of categories. Our main result is a probabilistic analog of the classic equivalence between the category of nominal sets and the Schanuel topos. Through this equivalence, we validate design decisions in prior work on probabilistic separation logic and create new connections to nominal-set-like models of probability.  more » « less
Award ID(s):
2220408
PAR ID:
10625332
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
ACM
Date Published:
ISBN:
9798400706608
Page Range / eLocation ID:
1 to 14
Format(s):
Medium: X
Location:
Tallinn Estonia
Sponsoring Org:
National Science Foundation
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