Concur : An Algorithm for Merging Concurrent Changes without Conflicts

Suppose you and I are both editing a document. You make and change and I make a change, concurrently. Now if we want to still be seeing the same document then I need to apply your change after mine and you mine after yours. But we can’t just apply them willy-nilly. I must amend yours somehow and you mine. If my change is written ∆, yours δ, my amended change δ.∆ and yours ∆.δ, we get ∗∆ ∗ ∆.δ = ∗δ ∗ δ.∆ as long as application is written ∗ and we don’t care about what we’re applying the changes to. We start by proving this identity for single changes and finish by proving it for many.