To ensure that functional programs preserve differential privacy, a key technique involves adding noise to the result according to the query’s sensitivity, which quantifies how much variations in the input can magnify the output. While prior work, like the Fuzz linear type system, focuses on global sensitivity for the L1 metric, we have extended it in two directions. First, to support vector metrics, and second, the main focus of this talk, to address local sensitivity. For the latter system, we provide a denotational semantics within the category of metric spaces, leveraging the recently introduced construction of a dependently graded comodule.