Soundness, Idempotence, and Commutativity of Set-Sharing

Title: Soundness, Idempotence, and Commutativity of Set-Sharing

Abstract: This research article focuses on the key properties of a standard abstract domain used in logic programming for sharing analysis, known as Sharing. The authors provide a generalization of the abstraction function for Sharing that can be applied to any language, with or without the occurs-check. They prove the soundness, idempotence, and commutativity of abstract unification using this abstraction function.

Main Research Question: How can the soundness, idempotence, and commutativity of the Sharing abstract domain be proven for logic programming, particularly in the context of abstract unification?

Methodology: The authors propose a generalization of the abstraction function for Sharing that can be applied to any language, with or without the occurs-check. They use logical reasoning and mathematical proofs to demonstrate the soundness, idempotence, and commutativity of abstract unification using this abstraction function.

Results: The authors provide a generalized abstraction function for Sharing that can be applied to any language, with or without the occurs-check. They prove the soundness, idempotence, and commutativity of abstract unification using this abstraction function.

Implications: The results of this research have significant implications for the field of logic programming. By providing a generalized abstraction function for Sharing that can be applied to any language, with or without the occurs-check, the authors have expanded the applicability of this standard abstract domain. Furthermore, their proofs of soundness, idempotence, and commutativity for abstract unification using this abstraction function provide a solid mathematical foundation for the Sharing abstract domain.

Keywords: Abstract Interpretation, Logic Programming, Occurs-Check, Rational Trees, Set-Sharing

Link to Article: https://arxiv.org/abs/0102030v1 Authors: arXiv ID: 0102030v1