Just as intuitionistic proofs can be modeled by functions, linear logic proofs, being symmetric in the inputs and outputs, can be modeled by relations . However generic relations do not establish any functional dependence between the arguments, and therefore it is questionable whether they can be thought as reasonable generalizations of functions. On the other hand, in some situations one can speak in some precise sense about an implicit functional dependence defined by a relation. It turns out that it is (...) possible to model linear logic with implicit functions rather than general relations, an adequate language for such a semantics being differential calculus. This results in a non-degenerate model enjoying quite strong completeness properties. (shrink)