Relational Disjoint-Set Forests

Walter Guttmann 🌐

August 26, 2020

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

We give a simple relation-algebraic semantics of read and write operations on associative arrays. The array operations seamlessly integrate with assignments in the Hoare-logic library. Using relation algebras and Kleene algebras we verify the correctness of an array-based implementation of disjoint-set forests with a naive union operation and a find operation with path compression.

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BSD License

History

August 10, 2023
added matrix model of Peano structures and order-embedding from nat (revision 9933c1ff260f)
June 19, 2021
added path halving, path splitting, relational Peano structures, union by rank (revision 98c7aa03457d)

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Session Relational_Disjoint_Set_Forests

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× 
@article{Relational_Disjoint_Set_Forests-AFP,
  author  = {Walter Guttmann},
  title   = {Relational Disjoint-Set Forests},
  journal = {Archive of Formal Proofs},
  month   = {August},
  year    = {2020},
  note    = {\url{https://isa-afp.org/entries/Relational_Disjoint_Set_Forests.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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