Static analysis of logic programs for independent and parallelism
Journal of Logic Programming
Compile-time derivation of variable dependency using abstract interpretation
Journal of Logic Programming
Freeness analysis for logic programs—and correctness?
ICLP'93 Proceedings of the tenth international conference on logic programming on Logic programming
Proceedings of the eleventh international conference on Logic programming
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A Synergistic Analysis for Sharing and Groundness with Traces Linearity
ESOP '94 Proceedings of the 5th European Symposium on Programming: Programming Languages and Systems
Freeness, Sharing, Linearity and Correctness - All at Once
WSA '93 Proceedings of the Third International Workshop on Static Analysis
Set-Sharing is Redundant for Pair-Sharing
SAS '97 Proceedings of the 4th International Symposium on Static Analysis
Set-sharing is redundant for pair-sharing
Theoretical Computer Science
Decomposing Non-redundant Sharing by Complementation
SAS '99 Proceedings of the 6th International Symposium on Static Analysis
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It is important that practical data flow analysers are backed by reliably proven theoretical results. Abstract interpretation provides a sound mathematical framework and necessary generic properties for an abstract domain to be well-defined and sound with respect to the concrete semantics. In logic programming, the abstract domain Sharing is a standard choice for sharing analysis for both practical work and further theoretical study. In spite of this, we found that there were no satisfactory proofs for the key properties of commutativity and idempotence that are essential for Sharing to be well-defined and that published statements of the safeness property assumed the occur-check. This paper provides a generalisation of the abstraction function for Sharing that can be applied to any language, with or without the occur-check. The results for safeness, idempotence and commutativity for abstract unification using this abstraction function are given.