文章基本信息

标题：Denotational Aspects of Untyped Normalization by Evaluation
本地全文：下载
作者：Andrzej Filinski ; Henning Korsholm Rohde
期刊名称：BRICS Report Series
印刷版ISSN：0909-0878
出版年度：2005
卷号：12
期号：4
出版社：Aarhus University
摘要：We show that the standard normalization-by-evaluation construction for the simply-typed lambda_{beta eta}-calculus has a natural counterpart for the untyped lambda_beta-calculus, with the central type-indexed logical relation replaced by a "recursively defined'' invariant relation , in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation. In the untyped setting, not all terms have normal forms, so the normalization function is necessarily partial. We establish its correctness in the senses of soundness (the output term, if any, is in normal form and beta-equivalent to the input term); identification ( beta-equivalent terms are mapped to the same result); and completeness (the function is defined for all terms that do have normal forms). We also show how the semantic construction enables a simple yet formal correctness proof for the normalization algorithm, expressed as a functional program in an ML-like call-by-value language. Finally, we generalize the construction to produce an infinitary variant of normal forms, namely Böhm trees . We show that the three-part characterization of correctness, as well as the proofs, extend naturally to this generalization.