Handbook of logic in computer science (vol. 1)
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Programming with streams in Coq: a case study: the Sieve of Eratosthenes
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
A fixedpoint approach to (co)inductive and (co)datatype definitions
Proof, language, and interaction
Structural Recursive Definitions in Type Theory
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Codifying Guarded Definitions with Recursive Schemes
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
Type-based termination of recursive definitions
Mathematical Structures in Computer Science
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Inductive and Coinductive Components of Corecursive Functions in Coq
Electronic Notes in Theoretical Computer Science (ENTCS)
Using Structural Recursion for Corecursion
Types for Proofs and Programs
Coalgebraic Reasoning in Coq: Bisimulation and the λ-Coiteration Scheme
Types for Proofs and Programs
Filters on coinductive streams, an application to eratosthenes' sieve
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
The optimal fixed point combinator
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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In type theory based logical frameworks, recursive and corecursive definitions are subject to syntactic restrictions that ensure their termination and productivity. These restrictions however greately decrease the expressive power of the language. In this work we propose a general approach for systematically defining fixed points for a broad class of well given recursive definition. This approach unifies the ones based on well-founded order to the ones based on complete metrics and contractive functions, thus allowing for mixed recursive/corecursive definitions. The resulting theory, implemented in the Coq proof assistant, is quite simple and hence it can be used broadly with a small, sustainable overhead on the user.