Similarity and Bisimilarity for Countable Non-Determinism and Higher-Order Functions

This paper investigates operationally based theories of a simply typed functional programming language with countable non determinism The theories are based upon lower upper and convex variants of applicative similarity and bisimilarity and the main result presented here is that these relations are compatible The di erences between the relations are illustrated by simple examples and their con tinuity properties are discussed It is also shown that in some cases the addition of countable non determinism to a programming language with nite non determinism alters the theory of the language