A Mechanised Proof System for Relation Algebra using Display Logic

We describe an implementation of the Display Logic calculus for relation algebra as an Isabelle theory. Our implementation is the first mechanisation of any display calculus. The inference rules of Display Logic are coded directly as Isabelle theorems, thereby guaranteeing the correctness of all derivations. Our implementation generalises easily to handle other display calculi. It also provides a useful interactive proof assistant for relation algebras. We describe various tactics and derived rules developed for simplifying proof search, including an automatic cut-elimination procedure, and example theorems proved using Isabelle. We show how some relation algebraic theorems proved using our system can be put in the form of structural rules of Display Logic, facilitating later re-use. We then show how the implementation can be used to prove results comparing alternative formalizations of relation algebra from a proof-theoretic perspective.