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Name Binding is Easy with Hypergraphs
Alimujiang YASEN Kazunori UEDA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E101D
No.4
pp.11261140 Publication Date: 2018/04/01 Publicized: 2018/01/12 Online ISSN: 17451361
DOI: 10.1587/transinf.2017EDP7257 Type of Manuscript: PAPER Category: Software System Keyword: name binding, substitution, hypergraph rewriting, graph type, formal systems,
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Summary:
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 λcalculus to introduce our technique. Then we encode a more complex formal system called System F_{<:}, a polymorphic λcalculus 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 λcalculus, 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.

