We present a program logic for Pitts and Stark’s $$\nu $$ν-calculus, an extension of the call-by-value simply-typed $$\lambda $$λ-calculus with a mechanism for the generation of fresh names. Names can be compared for equality and inequality, producing programs with subtle observable properties. Hidden names produced by interactions between generation and abstraction are captured logically with a second-order quantifier over type contexts. We illustrate usage of the logic through reasoning about well-known difficult cases from the literature.