2 Linear Dependent Types and Sensitivity Analysis : DFuzz

Function sensitivity—how much a function output can change with respect to changes in the input—is a key property in many research areas. For instance, in the field of differential privacy, a common mechanism for making a (possibly non-private) query private involves establishing a bound on its sensitivity. One way to bound the sensitivity of functional programs is by using a type-based analysis combining linear indexed types and dependent types — the main concept behind DFuzz, a language for differentially private queries. In this paper we propose a type checking algorithm for the system of [1] to make this analysis automatic, by reducing sensitivity analysis to constraint solving — a solution to these constraints provides an upper bound on program sensitivity.

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