Non-deterministic Lazy It -calculus Vs It -caculus Non-deterministic Lazy -calculus Vs -calculus

We pursue the study of the embedding of the-calculus into the-calculus. Various lambda calculi with parallel and convergence testing facilities are examined and their expressiveness compared; j-a lazy calculus augmented with a non-deterministic choice operator and a convergence testing combinator, emerges as a suitable language to be encoded in. Through the use of closures for variables and abstractions, the process of substitution in j is managed in a semi-explicit way. The semantics associated to both j and are based on contextual testing preorders. We deene an encoding of j into ; we prove that it is adequate with respect to those semantics. However, the encoding is not fully-adequate; standard examples show that is still more discriminating than j.