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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| Veröffentlicht in: | Logical methods in computer science Jg. 16, Issue 4; H. 4 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Logical Methods in Computer Science Association
14.12.2020
Logical Methods in Computer Science e.V |
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| ISSN: | 1860-5974, 1860-5974 |
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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. |
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| 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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| Keywords | Implicit computational complexity basic feasible functionals |
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| Title | Theory of higher order interpretations and application to Basic Feasible Functions |
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