文章基本信息

标题：The Complexity of Principal Inhabitation
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作者：Andrej Dudenhefner ; Jakob Rehof
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：84
页码：15:1-15:14
DOI：10.4230/LIPIcs.FSCD.2017.15
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：It is shown that in the simply typed lambda-calculus the following decision problem of principal inhabitation is Pspace-complete: Given a simple type tau, is there a lambda-term N in beta-normal form such that tau is the principal type of N? While a Ben-Yelles style algorithm was presented by Broda and Damas in 1999 to count normal principal inhabitants (thereby answering a question posed by Hindley), it does not induce a polynomial space upper bound for principal inhabitation. Further, the standard construction of the polynomial space lower bound for simple type inhabitation does not carry over immediately. We present a polynomial space bounded decision procedure based on a characterization of principal inhabitation using path derivation systems over subformulae of the input type, which does not require candidate inhabitants to be constructed explicitly. The lower bound is shown by reducing a restriction of simple type inhabitation to principal inhabitation.
关键词：Lambda Calculus; Type Theory; Simple Types; Inhabitation; Principal Type; Complexity