### 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.

### License

BSD License

### History

June 19, 2021
  added path halving, path splitting, relational Peano structures, union by rank (revision 98c7aa03457d)

### Topics

- Computer science/Data structures

### Session Relational_Disjoint_Set_Forests

- Disjoint_Set_Forests
- More_Disjoint_Set_Forests
- Matrix_Peano_Algebras

### Depends on

- Aggregation Algebras

### Used by

- Relational Minimum Spanning Tree Algorithms

## Cite

×

Relational_Disjoint_Set_Forests-AFP

    @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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Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Aug 26, 2020 : Isabelle2020