Addressed term rewriting systems: application to a typed object calculus

  • Authors:

  • Daniel J. Dougherty;Pierre Lescanne;Luigi Liquori

  • Affiliations:

  • Department of Computer Science, Worcester Polytechnic Institute, Worcester, MA 01609 U.S.A.;Laboratoire de l'Informatique du Parallélisme, École Normale Supérieure de Lyon, 46, Allée d'Italie, 69364 Lyon 07, France;INRIA Sophia Antipolis FR-06902 France

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 2006

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Abstract

We present a formalism called addressed term rewriting systems, which can be used to model implementations of theorem proving, symbolic computation and programming languages, especially aspects of sharing, recursive computations and cyclic data structures. Addressed Term Rewriting Systems are therefore well suited to describing object-based languages, and as an example we present a language called $\lambda{\cal O}bj^{a}$, incorporating both functional and object-based features. As a case study in how reasoning about languages is supported in the ATRS formalism, we define a type system for $\lambda{\cal O}bj^{a}$ and prove a type soundness result.