Iteration theories: the equational logic of iterative processes
Iteration theories: the equational logic of iterative processes
Axiomatizing iteration categories
Acta Cybernetica
Theoretical Computer Science
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TAPSOFT '89/CAAP '89 Proceedings of the International Joint Conference on Theory and Practice of Software Development, Volume 1: Advanced Seminar on Foundations of Innovative Software Development I and Colloquium on Trees in Algebra and Programming
Recursion and corecursion have the same equational logic
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Theoretical Computer Science
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LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
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Mathematical Structures in Computer Science
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Elgot theories: A new perspective on the equational properties of iteration
Mathematical Structures in Computer Science
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Iterative monads of Calvin Elgot were introduced to treat the semantics of recursive equations purely algebraically. They are Lawvere theories with the property that all ideal systems of recursive equations have unique solutions. We prove that the unique solutions in iterative monads satisfy all the equational properties of iteration monads of Stephen Bloom and Zoltan Esik, whenever the base category is hyper-extensive and locally finitely presentable. This result is a step towards proving that functorial iteration monads form a monadic category over sets in context. This shows that functoriality is an equational property when considered w.r.t. sets in context.