We study a l-calculus enriched with a non-deterministic choice combinator. We show that this combinator is adequately interpreted as the join in a canonical lattice of (parallel) continuous functions. The canonical model is in fact a logical one, concretely presented in a "typing system". Having established the complteness of this system, we show that the canonical interpretation provides us with a fully abstract model of the l-calculus with join. The proof of completeness relies upon the definability of the finite points of the logical domain
