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We present the spinal atomic \(\lambda \)-calculus, a typed \(\lambda \)-calculus with explicit sharing and atomic duplication that achieves spinal full laziness: duplicating only the direct paths between a binder and bound variables is enough for beta reduction to proceed. We show this calculus is the result of a Curry–Howard style interpretation...
The aim is to explore an efficient non-optimal implementation of the λ-calculus by developing atomic graphs: a graph rewriting system based on the atomic λ-calculus. The use of director annotations help guide active sharings through the graph, and the use of gates to maintain annotations after β-reduction. The use of labels and gates are the same...