コンピュータ ソフトウェア
Print ISSN : 0289-6540
λ2計算からλ計算への還元のための枠組み
藤田 憲悦
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2011 年 28 巻 4 号 p. 4_341-4_357

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We provide a framework that enables systematic proofs of the undecidability for type-related problems of λ (minimal logic with negation, conjunction and 2nd order existential types) from the corresponding undecidability results for those of λ2 (polymorphic lambda-calculus). This framework is applicable to various styles of the system λ, e.g., Church, domain-free, type-free, and Curry styles. The framework essentially relies on two properties: (1) the commutativity of type-forgetful (type-erasing) mappings and translations between λ2 and λ; and (2) the lifting of terms to increasingly well-defined terms having the proper type information. The translations are called CPS-translations, and the definitions are lifted to derivations from terms. Based on this approach, the following problems of λ are shown to be undecidable: (i) the typability problem in the (full) Church style, (ii) the typability and type checking problems in the type-free style, and (iii) the type checking problem in the Curry style. Finally, we observe an interesting correspondence to CPS-translated semi-unification problems.

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© 日本ソフトウェア科学会 2011
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