Coinduction All the Way Up

We revisit coinductive proof principles from a lattice theoretic point of view. By associating to any monotone function a function which we call the companion, we give a new presentation of both Knaster-Tarski's seminal result, and of the more recent theory of enhancements of the coinductive pr...

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Bibliographic Details
Published in:Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science pp. 307 - 316
Main Author: Pous, Damien
Format: Conference Proceeding
Language:English
Published: New York, NY, USA ACM 05.07.2016
Series:ACM Conferences
Subjects:
Theory of computation > Logic
Theory of computation > Semantics and reasoning
Coinduction
Parameterized coinduction
GSOS
Enhancements
Complete lattices
ISBN:9781450343916, 1450343910
Online Access:Get full text
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Summary:We revisit coinductive proof principles from a lattice theoretic point of view. By associating to any monotone function a function which we call the companion, we give a new presentation of both Knaster-Tarski's seminal result, and of the more recent theory of enhancements of the coinductive proof method (up-to techniques). The resulting theory encompasses parameterized coinduction, as recently proposed by Hur et al., and second-order reasoning, i.e., the ability to reason coinductively about the enhancements themselves. It moreover resolves a historical peculiarity about up-to context techniques. Based on these results, we present an open-ended proof system allowing one to perform proofs on-the-fly and to neatly separate inductive and coinductive phases.
ISBN:9781450343916
1450343910
DOI:10.1145/2933575.2934564