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...

Full description

Saved in:
Bibliographic Details
Published inProceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science pp. 307 - 316
Main Author Pous, Damien
Format Conference Proceeding
LanguageEnglish
Published New York, NY, USA ACM 05.07.2016
SeriesACM Conferences
Subjects
Theory of computation > Logic
Theory of computation > Semantics and reasoning
Coinduction
Parameterized coinduction
GSOS
Enhancements
Complete lattices
Online AccessGet full text
ISBN9781450343916
1450343910
DOI10.1145/2933575.2934564

Cover

More Information
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