Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.   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,  study program sensitivity and metric preservation from a denotational point of view. In particular,  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.  demonstrate metric CPOs by giving a model for the deterministic fragment of Fuzz.
['Arthur Azevedo de Amorim', 'Marco Gaboardi', 'Justin Hsu', 'Shin-ya Katsumata', 'Ikram Cherigui']
I am writing a research paper on a idea A semantic account of metric preservation
[{"from": "human", "value": "I am writing a research paper on a idea A semantic account of metric preservation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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  \ufffd\u00b7  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,  study program sensitivity and metric preservation from a denotational point of view. In particular,  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.  demonstrate metric CPOs by giving a model for the deterministic fragment of Fuzz."}]