Higher-Order Interpretations and Program Complexity

Patrick Baillot 1 Ugo Dal Lago 2, 3
3 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
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. 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 the notion of simply-typed term rewriting systems, we define higher-order polynomial interpretations for them and 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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Patrick Baillot, Ugo Dal Lago. Higher-Order Interpretations and Program Complexity. 21st Annual Conference of the EACSL, Computer Science Logic 2012 (CSL), Sep 2012, Fontainebleau, France. pp.62-76, ⟨10.4230/LIPIcs.CSL.2012.62⟩. ⟨hal-00798298⟩



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