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Interpretation methods and their restrictions to polynomials have been deeplyused to control the termination and complexity of first-order term rewritesystems. This paper extends interpretation methods to a pure higher orderfunctional language. We develop a theory of higher order functions that iswell-suited for the complexity analysis of this programming language. Theinterpretation domain is a complete lattice and, consequently, we expressprogram interpretation in terms of a least fixpoint. As an application, bybounding interpretations by higher order polynomials, we characterize BasicFeasible Functions at any order.

Theory of higher order interpretations and application to Basic Feasible Functions