A theory for program and data type specification
Theoretical Computer Science - Selected papers on theoretical issues of design and implementation of symbolic computation systems
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Control flow semantics
Vicious circles: on the mathematics of non-wellfounded phenomena
Vicious circles: on the mathematics of non-wellfounded phenomena
Final Semantics for untyped lambda-calculus
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Coinductive Axiomatization of Recursive Type Equality and Subtyping
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Codifying Guarded Definitions with Recursive Schemes
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
An Application of Co-inductive Types in Coq: Verification of the Alternating Bit Protocol
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
On the Foundation of Final Semantics: Non-Standard Sets, Metric Spaces, Partial Orders
Proceedings of the REX Workshop on Sematics: Foundations and Applications
Final Semantics for a Higher Order Concurrent Language
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
Universal coalgebra: a theory of systems
Universal coalgebra: a theory of systems
A Calculus of Circular Proofs and Its Categorical Semantics
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
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We introduce a coinductive logical system à la Gentzen for establishing bisimulation equivalences on circular non-wellfounded regular objects, inspired by work of Coquand, and of Brandt and Henglein. In order to describe circular objects, we utilize a typed language, whose coinductive types involve disjoint sum, cartesian product, and finite powerset constructors. Our system is shown to be complete with respect to a maximal fixed point semantics. It is shown to be complete also with respect to an equivalent final semantics. In this latter semantics, terms are viewed as points of a coalgebra for a suitable endofunctor on the category Set* of non-wellfounded sets. Our system subsumes an axiomatization of regular processes, alternative to the classical one given by Milner.