A semantic account of metric preservation
Arthur Azevedo de Amorim, Marco Gaboardi, Justin Hsu, Shin-ya Katsumata, Ikram Cherigui · 2016
Program sensitivity measures how robust a program is to small changes in its input, and is a fundamental notion in domains ranging from differential privacy to cyber-physical systems. A natural way to formalize program sensitivity is in terms of metrics on the input and output spaces, requiring that an r-sensitive function map inputs that are at distance d to outputs that are at distance at most r · d. Program sensitivity is thus an analogue of Lipschitz continuity for programs.