Name binding is easy with hypergraphs

Alimujiang Yasen, Kazunori Ueda

    Research output: Contribution to journalArticle

    Abstract

    We develop a technique for representing variable names and name binding which is a mechanism of associating a name with an entity in many formal systems including logic, programming languages and mathematics. The idea is to use a general form of graph links (or edges) called hyperlinks to represent variables, graph nodes as constructors of the formal systems, and a graph type called hlground to define substitutions. Our technique is based on simple notions of graph theory in which graph types ensure correct substitutions and keep bound variables distinct. We encode strong reduction of the untyped λ-calculus to introduce our technique. Then we encode a more complex formal system called System F<:, a polymorphic λ-calculus with subtyping that has been one of important theoretical foundations of functional programming languages. The advantage of our technique is that the representation of terms, definition of substitutions, and implementation of formal systems are all straightforward. We formalized the graph type hlground, proved that it ensures correct substitutions in the λ-calculus, and implemented hlground in HyperLMNtal, a modeling language based on hypergraph rewriting. Experiments were conducted to test this technique. By this technique, one can implement formal systems simply by following the steps of their definitions as described in papers.

    Original languageEnglish
    Pages (from-to)1126-1140
    Number of pages15
    JournalIEICE Transactions on Information and Systems
    VolumeE101D
    Issue number4
    DOIs
    Publication statusPublished - 2018 Apr 1

    Keywords

    • Formal systems
    • Graph type
    • Hypergraph rewriting
    • Name binding
    • Substitution

    ASJC Scopus subject areas

    • Software
    • Hardware and Architecture
    • Computer Vision and Pattern Recognition
    • Electrical and Electronic Engineering
    • Artificial Intelligence

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