I am having a difficulty in deciding the scope of the left-most lambda in the following expression.
I have learnt that we should put brackets in such a way that the scope of lambda will be maximum. So arrived at candidate- answer 1, below.
On the other hand, since the expression
(λuv.v)(λab.a)(λcd.c) does not contain any x, if we put brackets as in answer 2, still we are not changing the scope, right?
But I know that these two answers are not equivalent. So which one is the correct one?
The two candidate answers are:
I came up with this confusion through the tutorial: A Tutorial Introduction to the Lambda Calculus by Raul Rojas. There, in page 6, ~T is given as
λx.x(λuv.v)(λab.a)(λcd.c). If we apply brackets as in my answer-1, we will not be able to evaluate ~T to F.