Proof-Relevant Logical Relations for Name Generation

Pitts and Stark’s ν-calculus is a paradigmatic total language for studying the problem of contextual equivalence in higher-order languages with name generation. Models for the ν-calculus that validate basic equivalences concerning names may be constructed using functor categories or nominal sets, with a dynamic allocation monad used to model computations that may allocate fresh names. If recursion is added to the language and one attempts to adapt the models from (nominal) sets to (nominal) domains, however, the direct-style construction of the allocation monad no longer works. This issue has previously been addressed by using a monad that combines dynamic allocation with continuations, at some cost to abstraction.