SIGPLAN '86 Proceedings of the 1986 SIGPLAN symposium on Compiler construction
Partially Typed Terms between Church-Style and Curry-Style
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Information and Computation
Existential Type Systems with No Types in Terms
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
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Polymorphic type systems combine the reliability and efficiency of static type-checking with the flexibility of dynamic type checking. Unfortunately, such languages tend to be unwieldy unless they accommodate omission of much of the information necessary to perform type checking. The automatic inference of omitted type information has emerged as one of the fundamental new implementation problems of these languages. We show here that a natural formalization of the problem is undecidable. The proof is directly applicable to some practical situations, and provides a partial explanation of the difficulties encountered in other cases.