Typechecking is Undecidable when 'Type' is a Type
Name
MIT-LCS-TR-458.pdf
Size
2.19 MB
Format
Adobe PDF
Checksum (MD5)
7b6e78e5bdcdbbe7007f9b8681eff318
Author(s)
Reinhold, Mark B.
Date Issued
December 1989
Series/Report no.
MIT-LCS-TR-458
Abstract
A function has a dependent type when the type of its result depends upon the value of its argument. The type of all types is the type of every type, including itself. In a typed l-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.
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