Higher-order interpretations and program complexity
Polynomial interpretations and their generalizations like quasi-interpretations have been used in the setting of first-order functional languages to design criteria ensuring statically some complexity bounds on programs [10]. This fits in the area of implicit computational complexity, which aims at...
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| Published in: | Information and computation Vol. 248; pp. 56 - 81 |
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01.06.2016
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| Abstract | Polynomial interpretations and their generalizations like quasi-interpretations have been used in the setting of first-order functional languages to design criteria ensuring statically some complexity bounds on programs [10]. This fits in the area of implicit computational complexity, which aims at giving machine-free characterizations of complexity classes. In this paper, we extend this approach to the higher-order setting. For that we consider simply-typed term rewriting systems [35], we define higher-order polynomial interpretations for them, and we give a criterion ensuring that a program can be executed in polynomial time. In order to obtain a criterion flexible enough to validate interesting programs using higher-order primitives, we introduce a notion of polynomial quasi-interpretations, coupled with a simple termination criterion based on linear types and path-like orders. |
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| AbstractList | Polynomial interpretations and their generalizations like quasi-interpretations have been used in the setting of first-order functional languages to design criteria ensuring statically some complexity bounds on programs [10]. This fits in the area of implicit computational complexity, which aims at giving machine-free characterizations of complexity classes. In this paper, we extend this approach to the higher-order setting. For that we consider simply-typed term rewriting systems [35], we define higher-order polynomial interpretations for them, and we give a criterion ensuring that a program can be executed in polynomial time. In order to obtain a criterion flexible enough to validate interesting programs using higher-order primitives, we introduce a notion of polynomial quasi-interpretations, coupled with a simple termination criterion based on linear types and path-like orders. |
| Author | Dal Lago, Ugo Baillot, Patrick |
| Author_xml | – sequence: 1 givenname: Patrick surname: Baillot fullname: Baillot, Patrick email: patrick.baillot@ens-lyon.fr organization: Laboratoire d'Informatique du Parallélisme, Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, INRIA, Université Claude Bernard Lyon 1, France – sequence: 2 givenname: Ugo surname: Dal Lago fullname: Dal Lago, Ugo email: dallago@cs.unibo.it organization: Università di Bologna, Italy |
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| Keywords | Type systems Term rewriting systems Implicit computational complexity Lambda-calculus lambda-calculus type systems implicit computational complexity term rewriting systems |
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