Handbook of logic in computer science (vol. 2)
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
Higher-Order and Symbolic Computation
Structural Recursive Definitions in Type Theory
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
A short and flexible proof of Strong Normalization for the Calculus of Constructions
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
COLOG '88 Proceedings of the International Conference on Computer Logic
Dependent Types for Program Termination Verification
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Type-based termination of recursive definitions
Mathematical Structures in Computer Science
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Modelling general recursion in type theory
Mathematical Structures in Computer Science
Defining and reasoning about recursive functions: a practical tool for the coq proof assistant
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
Practical inference for type-based termination in a polymorphic setting
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Decidability of type-checking in the calculus of algebraic constructions with size annotations
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Union of Reducibility Candidates for Orthogonal Constructor Rewriting
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Implementing a normalizer using sized heterogeneous types
Journal of Functional Programming
Strong normalization and equi-(co)inductive types
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Mixed inductive/coinductive types and strong normalization
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
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
Automated termination analysis for programs with second-order recursion
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Rewriting Computation and Proof
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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Sized types provides a type-based mechanism to enforce termination of recursive definitions in typed λ-calculi. Previous work has provided strong indications that type-based termination provides an appropriate foundation for proof assistants based on type theory; however, most work to date has been confined to non-dependent type systems. In this article, we introduce a variant of the Calculus of Inductive Constructions with sized types and study its meta theoretical properties: subject reduction, normalization, and thus consistency and decidability of type-checking and of size-inference. A prototype implementation has been developed alongside case studies.