Optimizing optimal reduction

Abstract

We propose a type inference algorithm for lambda terms in elementary affine logic (EAL). The algorithm decorates the syntax tree of a simple typed lambda term and collects a set of linear constraints. The result is a parametric elementary type that can be instantiated with any solution of the set of collected constraints.We point out that the typeability of lambda terms in EAL has a practical counterpart, since it is possible to reduce any EAL-typeable lambda terms with the Lamping's abstract algorithm obtaining a substantial increase of performances.We show how to apply the same techniques to obtain decorations of intuitionistic proofs into linear logic proofs.