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The class of Basic Feasible Functionals BFF$_2$ is the type-2 counterpart ofthe class FP of type-1 functions computable in polynomial time. Severalcharacterizations have been suggested in the literature, but none of thesepresent a programming language with a type system guaranteeing this complexitybound. We give a characterization of BFF$_2$ based on an imperative languagewith oracle calls using a tier-based type system whose inference is decidable.Such a characterization should make it possible to link higher-order complexitywith programming theory. The low complexity (cubic in the size of the program)of the type inference algorithm contrasts with the intractability of theaforementioned methods and does not overly constrain the expressive power ofthe language.

A tier-based typed programming language characterizing Feasible Functionals