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Higher-Order Interpretations and Program Complexity Baillot, Patrick Dal Lago, Ugo implicit complexity higher-order rewriting quasi-interpretations 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Patrick Baillot and Ugo Dal Lago 2012 Is Part Of LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2012.62 urn:nbn:de:0030-drops-36641 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.62 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode