Optimizing optimal reduction: A type inference algorithm for elementary affine logic

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\u2019s 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

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