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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Existential Type Systems with No Types in Terms
verfasst von : Ken-etsu Fujita, Aleksy Schubert
Erschienen in: Typed Lambda Calculi and Applications
Verlag: Springer Berlin Heidelberg
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We study type checking, typability, and type inference problems for type-free style and Curry style second-order existential systems where the type-free style differs from the Curry style in that the terms of the former contain information on where the existential quantifier elimination and introduction take place but omit the information on which types are involved. We show that all the problems are undecidable employing reduction of second-order unification in case of the type-free system and semiunification in case of the Curry style system. This provides a fine border between problems yielding to a reduction of second-order unification problem and the semiunification problem. In addition, we investigate the subject reduction property of the system in the Curry-style.