Using a Generalisation Critic to find Bisimulations for Coinductive Proofs

Dennis, Louise Abigail; Bundy, Alan; Green, Ian

Abstract

Coinduction is a method of growing importance in reasoning about functional languages, due to the increasing prominence of lazy data structures. Through the use of bisimulations and proofs that bisimilarity is a congruence in various domains it can be used to prove the congruence of two processes.

A coinductive proof requires a relation to be chosen which can be proved to be a bisimulation. We use proof planning to develop a heuristic method which automatically constucts a candidate relation. If this relation doesn't allow the proof to go through a proof critic analyses the reasons why it failed and modifies the relation accordingly.

Several proof tools have been developed to aid coinductive proofs but all require user interaction. Crucially they require the user to supply an appropriate relation which the system can then prove to be a bisimulation.

Citation

Dennis, L. A., Bundy, A., & Green, I. Using a Generalisation Critic to find Bisimulations for Coinductive Proofs. Presented at 14th International Conference on Automated Deduction (CADE-14)

• Conference Name: 14th International Conference on Automated Deduction (CADE-14)
• Publication Date: Jan 1, 1999
• Deposit Date: Dec 8, 2005
• Publicly Available Date: Oct 9, 2007
• Peer Reviewed: Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/1023912
• Additional Information: Lecture Notes in Artificial Intelligence 1294