Bunched Fuzz: Sensitivity for Vector Metrics

Abstract Program sensitivity measures the distance between outputs of a program when run on two related inputs. This notion, which plays key role in areas such as data privacy and optimization, has been focus several analysis techniques introduced recent years. Among most successful ones, we can highlight type systems inspired by linear logic, pioneered Reed Pierce Fuzz programming language. In Fuzz, each is equipped with its own distance, boils down to checking. particular, features product types, corresponding different notions distance: tensor combines distances component adding them, while takes their maximum . this work, show that these products be generalized arbitrary $$L^p$$ L p , metrics are often used optimization. The original products, with, correspond special cases $$L^1$$ 1 $$L^\infty $$ ∞ To ease handling extend system bunches —as logic bunched implications—where groups variables combined using distances. We our extension reason about quantitative properties probabilistic programs.