文章基本信息

标题：The Undecidability of Type Related Problems in Type-free Style System F
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作者：Ken-Etsu Fujita ; Aleksy Schubert
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2010
卷号：6
页码：103-118
DOI：10.4230/LIPIcs.RTA.2010.103
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We consider here a number of variations on the System F, that are predicative second-order systems whose terms are intermediate between the Curry style and Church style. The terms here contain the information on where the universal quantifier elimination and introduction in the type inference process must take place, which is similar to Church forms. However, they omit the information on which types are involved in the rules, which is similar to Curry forms. In this paper we prove the undecidability of the type-checking, type inference and typability problems for the system. Moreover, the proof works for the predicative version of the system with finitely stratified polymorphic types. The result includes the bounds on the Leivant's level numbers for types used in the instances leading to the undecidability.
关键词：Lambda calculus and related systems; type checking; typability; partial type inference; 2nd order unification; undecidability; Curry style type system