The Rho Cube - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2001

The Rho Cube


The rewriting calculus, or Rho Calculus, is a simple calculus that uniformly integrates abstraction on patterns and non-determinism. Therefore, it fully integrates rewriting and lambda-calculus. The original presentation of the calculus was untyped. In this paper we present a uniform way to decorate the terms of the calculus with types. This gives raise to a new presentation a la Church, together with nine (8+1) type systems which can be placed in a rho-cube that extends the lambda-cube of Barendregt. Due to the matching capabilities of the calculus, the type systems use only one abstraction mechanism and therefore gives an original answer to the identification of the standard ``lambda'' and ``Pi'' abstractors. As a consequence, this brings matching and rewriting as the first class concepts of the Rho-versions of the Logical Framework (LF) of Harper-Honsell-Plotkin, and of the Calculus of Constructions (CC) of Coquand-Huet.
Fichier principal
Vignette du fichier
A01-R-202.pdf (300.59 Ko) Télécharger le fichier

Dates and versions

inria-00107877 , version 1 (19-10-2006)



Horatiu Cirstea, Claude Kirchner, Luigi Liquori. The Rho Cube. 4th International Conference on Foundations of Software Science and Computation Structures - FOSSACS 2001, Apr 2001, Genova, Italy. 15 p, ⟨10.1007/3-540-45315-6_11⟩. ⟨inria-00107877⟩
209 View
108 Download



Gmail Facebook Twitter LinkedIn More