A Unified Approach to Fully Lazy Sharing

We give an axiomatic presentation of sharing-via-labelling for weak lambda-calculi, that allows to formally compare many different approaches to fully lazy sharing, and obtain two important results. We prove that the known implementations of full laziness are all equivalent in terms of the number of beta-reductions performed, although they behave differently regarding the duplication of terms. We establish a link between the optimality theories of weak lambda-calculi and first-order rewriting systems by expressing fully lazy lambda-lifting in our framework, thus emphasizing the first-order essence of weak reduction