Abstract

We reformulate 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. Keywords: linear logic, data structures. 1 Introduction A multiplicative proof net is a graph representation of a multiplicative linear logic derivation [5]. 1 The proof net N corresponding to the derivation P is a (directed) hypergraph with a link (i.e., an hyperedge) for each rule and a vertex for each formula occurrence s.t. every link of N connects the active formulas of the corresponding rule of P. For instance, let P be a cut-free derivation using atomic axioms only and ending with the sequent ` A; the corresponding proof net N is the syntax tree of the formula A, plus a set of connections between pairs of oc...

Citations

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