Size-based termination of higher-order rewriting. F. Blanqui. 70 pages, submitted on Dec. 2015, revised in Jan. 2017 and Nov. 2017.
We provide a general and modular criterion for the termination of simply-typed λ-calculus extended with function symbols defined by user-defined rewrite rules. Following a work of Hughes, Pareto and Sabry for functions defined with a fixpoint operator and pattern-matching, several criteria use typing rules for bounding the height of arguments in function calls. In this paper, we extend this approach to rewriting-based function definitions and more general user-defined notions of size.