Fully abstract semantics of λμ in the π-calculus

We study the λμ-calculus, extended with explicit substitution, and study a logic-based compositional output-based translation into a variant of the π-calculus with pairing that preserves single-step explicit head reduction with respect to contextual equivalence. We will define two notions of equality for λμ, modelling explicit head-reduction, head reduction, and show they coincide. We define four notions of equivalence, two as extensions of the equalities, one based on reduction (considering terms without head-normal form equivalent as well), and one based on approximation, and show they all coincide. We will also define four notions of weak equivalence, where now we consider terms without weak head-normal form equivalent, that all coincide as well. We will then show full abstraction results for our translation for the weak equivalences with respect to contextually equivalence on processes.