Interaction of lexical and derivational semantics ---for example substitution and lambda conversion--- is typically a part of the on-line interpretation process. Proof-nets are to categorial grammar what phrase markers are to phrase structure grammar: unique graphical structures underlying equivalence classes of sequential syntactic derivations; but the role of proof-nets is deeper since they integrate also semantics. In this paper we show how interaction of lexical and derivational semantics at the lexico-syntactic interface can be precomputed as a process of off-line lexical compilation comprising Cut elimination in partial proof-nets.