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.
On 21 Jun 2009, at 21:12, Miguel Mitrofanov wrote:
An answer would probably depend on the reductions order you've
chosen. Would that do?
(\e -> e (\u -> e (\v -> u))) (\f -> \x -> f x) -- all variables
have different names, see?
= (\f -> \x -> f x) (\u -> (\f -> \x -> f x) (\v -> u))
= \x -> (\u -> (\f -> \x -> f x) (\v -> u)) x
= \x -> (\f -> \x -> f x) (\v -> x)
= \x -> \x -> (\v -> x) x -- Ouch!
= \x -> \x -> x
= \x -> id
where the real answer is
\x -> (\f -> \x -> f x) (\v -> x)
= \x -> (\f -> \y -> f y) (\v -> x)
= \x -> \y -> (\v -> x) y
= \x -> \y -> x
= \x -> const x
On 21 Jun 2009, at 20:53, Andrew Coppin wrote:
OK, so I'm guessing there might be one or two (!) people around
here who know something about the Lambda calculus.
I've written a simple interpretter that takes any valid Lambda
expression and performs as many beta reductions as possible. When
the input is first received, all the variables are renamed to be
unique.
Question: Does this guarantee that the reduction sequence will
never contain name collisions?
I have a sinking feeling that it does not. However, I can find no
counter-example as yet. If somebody here can provide either a proof
or a counter-example, that would be helpful.
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