Church => Scott = Ptime: an application of resource sensitive realizability

We introduce a variant of linear logic with second order quantifiers and type fixpoints, both restricted to purely linear formulas. The Church encodings of binary words are typed by a standard non-linear type ‘Church,’ while the Scott encodings (purely linear rep resentations of words) are by a linear type ‘Scott.’ We give a characterization of polynomial time func tions, which is derived from (Leivant and Marion 93): a function is computable in polynomial time if and only if it can be represented by a term of type Church ) Scott. To prove soundness, we employ a resource sensitive realizability technique developed by Hofmann and Dal Lago.