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...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Logical Methods in Computer Science e.V.
2020-12-01
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Series: | Logical Methods in Computer Science |
Subjects: | |
Online Access: | https://lmcs.episciences.org/4237/pdf |
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. |
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ISSN: | 1860-5974 |