Coinduction All the Way Up

Damien Pous (1, 2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages

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 parametrised 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 an 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.

Mots clés: Parametrised coinduction; GSOS; Complete lattices; Enhancements; Coinduction

Domaines: Informatique [cs]

Damien Pous. Coinduction All the Way Up. Thirty-First Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2016), Jul 2016, New York, United States. ⟨10.1145/2933575.2934564⟩. ⟨hal-01259622v2⟩