[Haskell-cafe] Slightly off-topic: Lambda calculus
Bertram Felgenhauer
bertram.felgenhauer at googlemail.com
Sun Jun 21 13:56:00 EDT 2009
Miguel Mitrofanov wrote:
> Correction: I think that one can find an expression that causes name
> clashes anyway, I'm just not certain that there is one that would clash
> independent of whichever order you choose.
Yes there is.
Consider
(\f g -> f (f (f (f (f (f g)))))) (\l a b -> l (b a)) (\x -> x)
which has 6 variables in total. This reduces to the normal form
\a b c d e f g -> g (f (e (d (c (b a)))))
which requires 7 variables. So without alpha-conversion at least one of
the original 6 variables will clash with itself.
Bertram
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