Research proof index

Overwriting one coordinate of a uniform function table is measure-preserving. Drawing a value u uniformly from R, then a full function table g : D → R uniformly, and returning Function.update g t u yields the same distribution as drawing the table directly. This is the t-marginal independence of the uniform (product) distribution on D → R:...

Restricting a uniform function table to a subdomain along an injection is uniform. For an injection e : A → B between finite types, drawing a uniform table g : B → R and restricting it along e (i.e. g ∘ e) yields the uniform distribution on A → R. This is the marginalization of the uniform (product) distribution on B → R onto the block of...