Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators
Logic in Computer Science
2015-07-01 v3 Discrete Mathematics
Abstract
The symmetric interaction combinators are an equally expressive variant of Lafont's interaction combinators. They are a graph-rewriting model of deterministic computation. We define two notions of observational equivalence for them, analogous to normal form and head normal form equivalence in the lambda-calculus. Then, we prove a full abstraction result for each of the two equivalences. This is obtained by interpreting nets as certain subsets of the Cantor space, called edifices, which play the same role as Boehm trees in the theory of the lambda-calculus.
Cite
@article{arxiv.0906.0380,
title = {Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators},
author = {Damiano Mazza},
journal= {arXiv preprint arXiv:0906.0380},
year = {2015}
}