Supporting Function Calls within PELCR

In [M. Pedicini and F. Quaglia. A parallel implementation for optimal lambda-calculus reduction PPDP '00: Proceedings of the 2nd ACM SIGPLAN international conference on Principles and practice of declarative programming, pages 3–14, ACM, 2000, M. Pedicini and F. Quaglia. PELCR: Parallel environment for optimal lambda-calculus reduction. CoRR, cs.LO/0407055, accepted for publication on TOCL, ACM, 2005], PELCR has been introduced as an implementation derived from the Geometry of Interaction in order to perform virtual reduction on parallel/distributed computing systems. In this paper we provide an extension of PELCR with computational effects based on directed virtual reduction [V. Danos, M. Pedicini, and L. Regnier. Directed virtual reductions. In M. Bezem D. van Dalen, editor, LNCS 1258, pages 76–88. EACSL, Springer Verlag, 1997], namely a restriction of virtual reduction [V. Danos and L. Regnier. Local and asynchronous beta-reduction (an analysis of Girard's EX-formula). LICS, pages 296–306. IEEE Computer Society Press, 1993], which is a particular way to compute the Geometry of Interaction [J.-Y. Girard. Geometry of interaction 1: Interpretation of system F. In R. Ferro, et al. editors Logic Colloquium '88, pages 221–260. North-Holland, 1989] in analogy with Lamping's optimal reduction [J. Lamping. An algorithm for optimal lambda calculus reduction. In Proc. of 17th Annual ACM Symposium on Principles of Programming Languages. ACM, San Francisco, California, pages 16–30, 1990]. Moreover, the proposed solution preserves scalability of the parallelism arising from local and asynchronous reduction as studied in [M. Pedicini and F. Quaglia. PELCR: Parallel environment for optimal lambda-calculus reduction. CoRR, cs.LO/0407055, accepted for publication on TOCL, ACM, 2005].