Inductive Definitions: Automation and Application
Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications
Fix-Point Equations for Well-Founded Recursion in Type Theory
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
Nested General Recursion and Partiality in Type Theory
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Recursive Function Definition over Coinductive Types
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Type-based termination of recursive definitions
Mathematical Structures in Computer Science
Inductive and Coinductive Components of Corecursive Functions in Coq
Electronic Notes in Theoretical Computer Science (ENTCS)
Fixed point semantics and partial recursion in Coq
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
Partial and Nested Recursive Function Definitions in Higher-order Logic
Journal of Automated Reasoning
A unifying approach to recursive and co-recursive definitions
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
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
Filters on coinductive streams, an application to eratosthenes' sieve
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
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In this paper, we develop a general theory of fixed point combinators, in higher-order logic equipped with Hilbert's epsilon operator. This combinator allows for a direct and effective formalization of corecursive values, recursive and corecursive functions, as well as functions mixing recursion and corecursion. It supports higher-order recursion, nested recursion, and offers a proper treatment of partial functions in the sense that domains need not be hardwired in the definition of functionals. Our work, which has been entirely implemented in Coq, unifies and generalizes existing results on contraction conditions and complete ordered families of equivalences, and relies on the theory of optimal fixed points for the treatment of partial functions. It provides a practical way to formalize circular definitions in higher-order logic.