{"id":610443,"date":"2019-09-24T10:09:22","date_gmt":"2019-09-24T17:09:22","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=610443"},"modified":"2019-11-04T19:02:58","modified_gmt":"2019-11-05T03:02:58","slug":"evaluating-lambda-terms-with-traversals-2","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/evaluating-lambda-terms-with-traversals-2\/","title":{"rendered":"Evaluating Lambda Terms with Traversals"},"content":{"rendered":"<p>A method to evaluate untyped lambda terms based on a term tree-traversing technique inspired by Game Semantics and judicious use of eta-expansion. As\u00a0<em>traversals<\/em>\u00a0explore nodes of the term tree, they dynamically eta-expand some of the subterms in order to locate their non-immediate arguments. A quantity called\u00a0<em>dynamic arity<\/em>\u00a0determines 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\u00a0<em>leftmost linear reduction<\/em>, a non-standard reduction strategy based on\u00a0<em>head linear reduction<\/em>\u00a0of Danos-Regnier.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A method to evaluate untyped lambda terms based on a term tree-traversing technique inspired by Game Semantics and judicious use of eta-expansion. As\u00a0traversals\u00a0explore nodes of the term tree, they dynamically eta-expand some of the subterms in order to locate their non-immediate arguments. A quantity called\u00a0dynamic arity\u00a0determines the necessary amount of eta-expansion to perform at a 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