Towards a Theory of Bisimulation for Local Names

Pitts and Stark have proposed the ν-calculus as a language for investigating the interaction of unique name generation and higherorder functions. They developed a sound model based on logical relations, but left completeness as an open problem. In this paper, we develop a complete model based on bisimulation for a labelled transition system semantics. We show that bisimulation is complete, but not sound, for the ν-calculus. We also show that by adding assignment to the ν-calculus, bisimulation becomes sound and complete. The analysis used to obtain this result illuminates the difficulties involved in finding fully abstract models for ν-calculus proper.