Atomic Lambda Calculus: A Typed Lambda-Calculus with Explicit Sharing

An explicit-sharing lambda-calculus is presented, based on a Curry-Howard-style interpretation of the deep inference proof formalism. Duplication of subterms during reduction proceeds `atomically', i.e. on individual constructors, similar to optimal graph reduction in the style of Lamping. The calculus preserves strong normalisation with respect to the lambda-calculus, and achieves fully lazy sharing.