Comparing λ-calculus translations in sharing graphs
Since Lamping's seminal work [Lam90] on optimal graph reduction techniques for the λ-calculus, several different translations based on the same set of control operators (sharing graphs) have been proposed in the literature [GAL92a, GAL92b, AL93a, As94]. In this paper we clarify the correspondence between all these translations, passing through the so called bus-notation [GAL92a]. Indeed all the sharing graph encodings turn out to be equivalent modulo the way of counting bus levels.
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- [As94]A. Asperti. Linear Logic, Comonads, and Optimal Reductions. To appear in Fundamenta Informaticae, Special Issue devoted to Categories in Computer Science. 1994.Google Scholar
- [AL93a]A. Asperti, C. Laneve. Optimal Reductions in Interaction Systems. Proc. of the 4th Joint Conference on the Theory and Practice of Software Development, TAPSOFT'93, Orsay (France). April 1993.Google Scholar
- [AL94]A. Asperti, C. Laneve. Interaction System 2: The practice of optimal reductions. May 1993. A revised version of this paper may be got by anonymous ftp at cma.cma.fr as file pub/papers/cosimo/newIS2.ps.Z.Google Scholar
- [ADLR94]A. Asperti, V. Danos, C. Laneve, L. Regnier. Paths in the λ-calculus: three years of communications without understandings. Proc. of the 9th Annual Symposium on Logic in Computer Science (LICS 94), Paris 1994.Google Scholar
- [DR93]V. Danos, L. Regnier. Local and asynchronous beta-reduction. Proc. of the 8th Annual Symposium on Logic in Computer Science (LICS 93), Montreal. 1993.Google Scholar
- [Gi86]J. Y. Girard. Linear Logic. Theoretical Computer Science, 50. 1986.Google Scholar
- [GAL92a]G. Gonthier, M. Abadi, J.J. Lévy. The geometry of optimal lambda reduction. Proc. of the 19th Symposium on Principles of Programming Languages (POPL 92). 1992.Google Scholar
- [GAL92b]G. Gonthier, M. Abadi, J.J. Lévy. Linear Logic without boxes. Proc. of the 7th Annual Symposium on Logic in Computer Science (LICS'92). 1992.Google Scholar
- [Lam90]J. Lamping. An algorithm for optimal lambda calculus reductions. Proc. of the 17th Symposium on Principles of Programming Languages (POPL 90). San Francisco. 1990.Google Scholar
- [Le78]J.J. Levy. Réductions correctes et optimales dans le lambda-calcul. Thèse de doctorat d'état, Université de Paris VII. 1978.Google Scholar
- [Re92]L. Regnier. Lambda Calcul et Réseaux. Thèse de doctorat, Université Paris VII. 1992.Google Scholar