Abstract
This paper presents a method to evaluate untyped lambda terms based on a term tree-traversing technique and judicious use of eta-expansion. The traversal method is inspired by Game Semantics. As traversals explore nodes of the term tree, they dynamically eta-expand some of the subterms to locate their non-immediate arguments. A quantity called dynamic arity determines the necessary amount of eta-expansion to perform at a given point. Traversals are finitely enumerable and characterize the paths in the tree representation of the beta-normal form when it exists. Correctness of the evaluation method follows from the fact that traversals implement leftmost linear reduction, a non-standard reduction strategy based on head linear reduction.
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