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Typechecking is Undecidable When 'Type' is a Type (1989)
by
Mark B. Reinhold
| Citations: | 5 - 0 self |
BibTeX
@TECHREPORT{Reinhold89typecheckingis,
author = {Mark B. Reinhold},
title = {Typechecking is Undecidable When 'Type' is a Type},
institution = {},
year = {1989}
}
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Abstract
A function has a dependent type when the type of its result depends upon the value of its argument. The type o all types is the type of every type, including itself. In a typed A-calculus, these two features synergize in a conceptually clean and uniform way to yield enormous expressive power at very little apparent cost. By reconstructing and analyzing a paradox due to Girard, we argue that there is no effective typechecking algorithm for such a language.
