Theory of higher order interpretations and application to Basic Feasible Functions
Logic in Computer Science
2023-06-22 v4 Computational Complexity
Programming Languages
Abstract
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.
Cite
@article{arxiv.1801.08350,
title = {Theory of higher order interpretations and application to Basic Feasible Functions},
author = {Emmanuel Hainry and Romain Péchoux},
journal= {arXiv preprint arXiv:1801.08350},
year = {2023}
}