Derivation and safety of an abstract unification algorithm for groundness and aliasing analysis

We derive and prove safe an abstract unification algorithm for groundness and aliasing analysis in logic programs. In general, proving the safety of abstract unification plays a crucial role in the construction of an abstract interpretation. We adopt a notion of abstract substitutions which is originally due to Sondergaard and derive an abstract unification algorithm by abstracting the process of unifying a pair of concrete atoms. This results in a concise and well motivated definition of abstract unification together with a proof of its safety. The resulting algorithm appears to formally reconstruct that intended by Sondergaard. The approach followed in deriving the algorithm is interesting in its own; to appreciate its advantages it is sufficient to compare our presentation of the algorithm with previous ones, and to note that those previous are not accompanied by proofs of safety.