Encoding the pure lambda calculus into hierarchical graph rewriting

Kazunori Ueda*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationRewriting Techniques and Applications - 19th International Conference, RTA 2008, Proceedings
Number of pages17
Publication statusPublished - 2008
Event19th International Conference on Rewriting Techniques and Applications, RTA 2008 - Hagenberg, Austria
Duration: 2008 Jul 152008 Jul 17

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5117 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Rewriting Techniques and Applications, RTA 2008

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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