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The Undecidability of Typability in the Lambda-Pi-Calculus

06/13/2023

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by Gilles Dowek, et al.

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The set of pure terms which are typable in the λΠ-calculus in a given context is not recursive. So there is no general type inference algorithm for the programming language Elf and, in some cases, some type information has to be mentioned by the programmer.

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