Theory of Higher Order Interpretations and Application to Basic Feasible Functions

Emmanuel Hainry (1) , Romain Péchoux (1)

1 MOCQUA - Designing the Future of Computational Models

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional language. We develop a theory of higher order functions that is well-suited for the complexity analysis of this programming language. The interpretation domain is a complete lattice and, consequently, we express program interpretation in terms of a least fixpoint. As an application, by bounding interpretations by higher order polynomials, we characterize Basic Feasible Functions at any order.

Mots clés: Implicit computational complexity; basic feasible functionals

Domaines: Complexité [cs.CC]; Informatique et langage [cs.CL]; Logique en informatique [cs.LO]

Emmanuel Hainry, Romain Péchoux. Theory of Higher Order Interpretations and Application to Basic Feasible Functions. Logical Methods in Computer Science, 2020, 16 (4), pp.25. ⟨10.23638/LMCS-16(4:14)2020⟩. ⟨hal-02499206v2⟩