Simulate Match and Mismatch by Computing in Pi-Calculus

Problem of expressiveness between lambda calculus and pi-calculus was still open these years. A full abstraction of lambda-calculus in pi-calculus, given by Cai and Fu, shows that a pi-def, a variant of pi-calculus, is powerful enough to be the target calculus instead of minimal pi-calculus, pi-M. In fact, there are some differences between these two calculi and the most important one is that pi-M contains no operator like match and mismatch, which makes pi-def more expressive. In this paper, a new approach is proposed that simulate, in the framework of pi-calculus, match and mismatch by computing and transforms-terms to a simpler form without match and mismatch. The encoding is also proved to reserve bisimulation and will be put into a part of an interpretation of lambda-calculus in pi-calculus.