Theory of higher order interpretations and application to Basic Feasible Functions

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 i...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 16, Issue 4; no. 4
Main Authors:	Hainry, Emmanuel, Péchoux, Romain
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science Association 14.12.2020 Logical Methods in Computer Science e.V
Subjects:	Computation and Language Computational Complexity Computer Science computer science - computational complexity computer science - logic in computer science computer science - programming languages Logic in Computer Science Implicit computational complexity basic feasible functionals
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	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.
ISSN:	1860-5974 1860-5974
DOI:	10.23638/LMCS-16(4:14)2020