Handbook of logic in computer science (vol. 2)
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
A Generic Normalisation Proof for Pure Type Systems
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
Let's see how things unfold: reconciling the infinite with the intensional
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
On strong normalization of the calculus of constructions with type-based termination
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Ultrametric Semantics of Reactive Programs
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
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
Practical inference for type-based termination in a polymorphic setting
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Pure type systems with corecursion on streams: from finite to infinitary normalisation
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming
Copatterns: programming infinite structures by observations
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Productivity of core cursive 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 core cursive 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 co inductive types.