Encoding the pure lambda calculus into hierarchical graph rewriting

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

    9 Citations (Scopus)

    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.

    Original languageEnglish
    Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Pages392-408
    Number of pages17
    Volume5117 LNCS
    DOIs
    Publication statusPublished - 2008
    Event19th International Conference on Rewriting Techniques and Applications, RTA 2008 - Hagenberg
    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)03029743
    ISSN (Electronic)16113349

    Other

    Other19th International Conference on Rewriting Techniques and Applications, RTA 2008
    CityHagenberg
    Period08/7/1508/7/17

      Fingerprint

    ASJC Scopus subject areas

    • Computer Science(all)
    • Biochemistry, Genetics and Molecular Biology(all)
    • Theoretical Computer Science

    Cite this

    Ueda, K. (2008). Encoding the pure lambda calculus into hierarchical graph rewriting. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5117 LNCS, pp. 392-408). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5117 LNCS). https://doi.org/10.1007/978-3-540-70590-1_27