Applicative Bisimulation and Quantum λ-Calculi

Abstract

Applicative bisimulation is a coinductive technique to check program equivalence in higher-order functional languages. It is known to be sound — and sometimes complete — with respect to context equivalence. In this paper we show that applicative bisimulation also works when the underlying language of programs takes the form of a linearλ-calculus extended with features such as probabilistic binary choice, but also quantum data, the latter being a setting in which linearity plays a role. The main results are proofs of soundness for the obtained notions of bisimilarity.