Type-Based Productivity of Stream Definitions in the Calculus of Constructions

Productivity of corecursive definitions is an essential property in proof assistants since it ensures logical consistency and decidability of type checking. Type-based mechanisms for ensuring productivity use types annotated with size information to track the number of elements produced in corecursive definitions. In this paper, we propose an extension of the Calculus of Constructions-the theory underlying the Coq proof assistant-with a type-based criterion for ensuring productivity of stream definitions. We prove strong normalization and logical consistency. Furthermore, we define an algorithm for inferring size annotations in types. These results can be easily extended to handle general coinductive types.