I need a little help with a lambda calculus reduction to normal form:$$(\lambda xxxx.xx)(\lambda x.xx)(\lambda x.x)y((\lambda x.x)x)$$It should be solved like this:$$xx(\lambda x.x)y((\lambda x.x)x)$$and then:$$xx(\lambda x.x)y(x)$$This is the result of any of the lambda calculators that you can find online.My question is: why can't I go on with reductions and make also $(\lambda x.x)y$ so the resulting expression would be $xxy(x)$?Can you give me a complete answer, with theory of lambda calculus rules/proofs?I really want to understand this exercise, any help would be appreciated.
Normal form Lambda calculus expression
lambda calculus;normal forms