Completeness of Conversion between Reactive Programs for Ultrametric Models

In 1970 Friedman proved completeness of beta eta conversion in the simply-typed lambda calculus for the set-theoretical model. Recently Krishnaswami and Benton have captured the essence of Hudak’s reactive programs in an extension of simply typed lambda calculus with causal streams and a temporal modality and provided this typed lambda calculus for reactive programs with a sound ultrametric semantics. We show that beta eta conversion in the typed lambda calculus of reactive programs is complete for the ultrametric model.