Encoding the Pure Lambda Calculus into Hierarchical Graph Rewriting

  • Kazunori Ueda
Conference paper

DOI: 10.1007/978-3-540-70590-1_27

Volume 5117 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Ueda K. (2008) Encoding the Pure Lambda Calculus into Hierarchical Graph Rewriting. In: Voronkov A. (eds) Rewriting Techniques and Applications. RTA 2008. Lecture Notes in Computer Science, vol 5117. Springer, Berlin, Heidelberg

Abstract

Fine-grained reformulation of the lambda calculus is expected to solve several difficulties with the notion of substitutions—definition, implementation and cost properties. However, previous attempts including those using explicit substitutions and those using Interaction Nets were not ideally simple when it came to the encoding of the pure (as opposed to weak) lambda calculus. This paper presents a novel, fine-grained, and highly asynchronous encoding of the pure lambda calculus using LMNtal, a hierarchical graph rewriting language, and discusses its properties. The major strength of the encoding is that it is significantly simpler than previous encodings, making it promising as an alternative formulation, rather than just the encoding, of the pure lambda calculus. The membrane construct of LMNtal plays an essential role in encoding colored tokens and operations on them. The encoding has been tested using the publicly available LMNtal implementation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Kazunori Ueda
    • 1
  1. 1.Dept. of Computer Science and EngineeringWaseda UniversityTokyoJapan