A Rho Cube - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports Year : 2000

A Rho Cube

Abstract

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.

Domains

Other [cs.OH]
No file

Dates and versions

inria-00099309 , version 1 (26-09-2006)

Identifiers

  • HAL Id : inria-00099309 , version 1

Cite

Horatiu Cirstea, Claude Kirchner, Luigi Liquori. A Rho Cube. [Intern report] A00-R-344 || cirstea00d, LORIA, UMR 7503, Université de Lorraine, CNRS, Vandoeuvre-lès-Nancy. 2000, 18 p. ⟨inria-00099309⟩
147 View
0 Download

Share

Gmail Facebook X LinkedIn More