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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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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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.
AbstractList 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.
Author Péchoux, Romain
Hainry, Emmanuel
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Issue 4
Keywords Implicit computational complexity
basic feasible functionals
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SubjectTerms 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
Title Theory of higher order interpretations and application to Basic Feasible Functions
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