Feasible computation in higher types

We study the notion of feasible functional of finite type. For type level 2, we consider the oracle Turing machine model, and examine Mehlhorn's class of feasible functionals for this model. We give a new characterization of Mehlhorn's class, using a generalization of polynomials to type 2, and consider extensions of Mehlhorn's class. For higher type levels, we introduce a new computational model using a programming language approach, and define a class of feasible functionals for this model which is a generalization of the type 2 feasible functionals to higher types.