Hashing Modulo Alpha-Equivalence

In many applications one wants to identify identical subtrees of a program syntax tree.  This identification should ideally be robust to alpha-renaming of the program, but no existing technique has been shown to achieve this with good efficiency (better than O(n^2) in expression size). We present a new, asymptotically efficient way to hash modulo alpha-equivalence. A key insight of our method is to use a weak (commutative) hash combiner at exactly one point in the construction, which admits an algorithm with O(n*(log n)^2) time complexity. We prove that the use of the commutative combiner nevertheless yields a strong hash with low collision probability.