A linear algorithm for MLL proof net correctness and sequentialization

Abstract

The paper presents in full detail the first linear algorithm given in the literature (Guerrini (1999) [6]) implementing proof structure correctness for multiplicative linear logic without units. The algorithm is essentially a reformulation of the Danos contractibility criterion in terms of a sort of unification. As for term unification, a direct implementation of the unification criterion leads to a quasi-linear algorithm. Linearity is obtained after observing that the disjoint-set union-find at the core of the unification criterion is a special case of union-find with a real linear time solution.