Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Proving the correctness of reactive systems using sized types
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The size-change principle for program termination
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Structural Recursive Definitions in Type Theory
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
A Generic Normalisation Proof for Pure Type Systems
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
CIC∧: type-based termination of recursive definitions in the calculus of inductive constructions
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Type-Based Productivity of Stream Definitions in the Calculus of Constructions
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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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.