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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| Vydané v: | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science s. 307 - 316 |
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| Hlavný autor: | |
| Médium: | Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
New York, NY, USA
ACM
05.07.2016
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| Edícia: | ACM Conferences |
| Predmet: | |
| ISBN: | 9781450343916, 1450343910 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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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| ISBN: | 9781450343916 1450343910 |
| DOI: | 10.1145/2933575.2934564 |