Relation-Algebraic Verification of Disjoint-Set Forests
For formal verification researchers, it provides a method to verify low-level array algorithms using high-level relation algebras, though it is an incremental extension of prior work.
This paper extends relation-algebraic verification to array-based implementations, proving correctness of disjoint-set forests with union-by-rank and path compression/splitting/halving in Isabelle/HOL.
This paper studies how to use relation algebras, which are useful for high-level specification and verification, for proving the correctness of lower-level array-based implementations of algorithms. We give a simple relation-algebraic semantics of read and write operations on associative arrays. The array operations seamlessly integrate with assignments in computation models supporting while-programs. As a result, relation algebras can be used for verifying programs with associative arrays. We verify the correctness of an array-based implementation of disjoint-set forests using the union-by-rank strategy and find operations with path compression, path splitting and path halving. All results are formally proved in Isabelle/HOL. This paper is an extended version of [1].