Observational Equivalence for the Interaction Combinators and Internal Separation

We define an observational equivalence for Lafont's interaction combinators, which we prove to be the least discriminating non-trivial congruence on total nets (nets admitting a deadlock-free normal form) respecting reduction. More interestingly, this equivalence enjoys an internal separation property similar to that of Böhm's Theorem for the λ-calculus.