Efficiency of a good but not linear nominal unification algorithm

Abstract

We present a nominal unification algorithm that runs in O(n × log(n) × G(n)) time, where G is the functional inverse of Ackermann's function. Nominal unification generates a set of variable assignments if there exists one, that makes terms involving binding operations α-equivalent. We preserve names while using special representations of de Bruijn numbers to enable efficient name management. We use Martelli-Montanari style multi-equation reduction to generate these name management problems from arbitrary unification terms.