@article {962666,
	title = {A Semantic Account of Metric Preservation},
	journal = {Symposium on the Principle of Programming Languages, ACM},
	year = {2017},
	month = {Jan 2017},
	abstract = {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\&nbsp;r-sensitive function map inputs that are at distance\&nbsp;d\&nbsp;to outputs that are at distance at most\&nbsp;r.d. Program sensitivity is thus an analogue of Lipschitz continuity for programs. Reed and Pierce introduced Fuzz, a functional language with a linear type system that can express program sensitivity. They show soundness operationally, in the form of a metric preservation property. Inspired by their work, we study program sensitivity and metric preservation from a denotational point of view. In particular, we introduce metric CPOs, a novel semantic structure for reasoning about computation on metric spaces, by endowing CPOs with a compatible notion of distance. This structure is useful for reasoning about metric properties of programs, and specifically about program sensitivity. We demonstrate metric CPOs by giving a model for the deterministic fragment of Fuzz.},
	url = {https://arxiv.org/abs/1702.00374},
	author = {Arthur Azevedo de Amorim and Marco Gaboardi and Justin Hsu and Shin-ya Katsumata and Ikram Cherigui}
}
