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Lambda Calculus - Reductions #4
Lambda Calculus - Reductions #4
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This expression can't be reduced further using the beta-rule because it's already in its simplest form. The beta-rule allows us to apply a function to an argument, but in this case, the expression doesn't contain any applications that can be further simplified.
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I think that it is kind of missleading to put in CAN'T REDUCE in quotes in the question body. I tried to submit it like that and it failed. Perhaps they should change it so it is more clear.
Note this problem trivially cannot be reduced to a "single term" since it the whole thing is a function, not a function application. The problem should probably be changed from
to something like
in order to actually be interesting. But let's look at the original anyway.
We can unroll the expression into a neater form: (Note I'm using the symbol "=" loosely here, but it is pretty unambiguous what I mean).
We clearly can replace f with g here, so we have
This certainly cannot be reduced; if we try to evaluate (b b), we obtain
and so on.