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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| Veröffentlicht in: | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science S. 307 - 316 |
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| Format: | Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY, USA
ACM
05.07.2016
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| Schriftenreihe: | ACM Conferences |
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| ISBN: | 9781450343916, 1450343910 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Pous, Damien |
| Author_xml | – sequence: 1 givenname: Damien surname: Pous fullname: Pous, Damien email: Damien.Pous@ens-lyon.fr organization: Université de Lyon, CNRS, ENS de Lyon, UCB Lyon, LIP |
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| DOI | 10.1145/2933575.2934564 |
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| Keywords | Coinduction Parameterized coinduction GSOS Enhancements Complete lattices |
| Language | English |
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| Snippet | 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,... |
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| SubjectTerms | Theory of computation -- Logic Theory of computation -- Semantics and reasoning |
| Title | Coinduction All the Way Up |
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