On Strong Normalization of the Calculus of Constructions with Type-Based Termination

Benjamin Grégoire 1 Jorge Sacchini 1
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Termination of recursive functions is an important property in proof assistants based on dependent type theories; it implies consistency and decidability of type checking. Type-based termination is a mechanism for ensuring termination that uses types annotated with size information to check that recursive calls are performed on smaller arguments. Our long-term goal is to extend the Calculus of Inductive Constructions with a type-based termination mechanism and prove its logical consistency. In this paper, we present an extension of the Calculus of Constructions (including universes and impredicativity) with sized natural numbers, and prove strong normalization and logical consistency. Moreover, the proof can be easily adapted to include other inductive types.
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Benjamin Grégoire, Jorge Sacchini. On Strong Normalization of the Calculus of Constructions with Type-Based Termination. 17th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Oct 2010, Yogyakarta, Indonesia. pp.333-347, ⟨10.1007/978-3-642-16242-8_24⟩. ⟨hal-00537104⟩

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