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.


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.


BSD License


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)


Session Relational_Disjoint_Set_Forests