Completeness of MLL proof-nets w.r.t. weak distributivity
Résumé
We examine 'weak-distributivity' (a.k.a. linear distributivity) as a rewriting rule WD defined on multiplicative proof-structures (so, in particular, on multiplicative proof-nets: MLL). This rewriting does not preserve the type of proof-nets, but does preserve their correctness. The specific contribution of this paper, is to give a direct proof of completeness for WD: starting from a set of simple generators (proof-nets which are a n-ary tensor of 'parized'-axioms), any mono-conclusion MLL proof-net can be reached by WD rewriting (up to tensor and par associativity and commutativity)