Question

Beta reduce the following lambda expressions, if possible:

a) (lambda x . lambda y. (x y) (y w))

b) (lambda x . (x x) lambda x . (x x))

Answer 1

answer to the above question are : -

a )

first expression can be solved using beta reduction, but we have to rename one y using alpha renaming to make one of the y free for substituition purpose.

a> tn. ty. (a y) (y w) here, second y is bound to dy and third y is fill so by possono form in E m) Eady. (ay) and = ly w) So, it can be simplified as :- dy. llyw) y). now bosh y are bound to dy which is wrong. so we do x-renaming of dy y de so that one of the y remains free. ио) Форчихіол иш la foto- (ax. dz. ( x 2) (y w)) now performing - reductedn, Sulistituting a mith (yw.) and adding parathesis fellegring left... a) assortihintay la bellab)c azolly w) 2)

b ) second expression is of non terminating form which means on solving it will follow infinte loop pattern.so it cant be solved.

if my answer helped then please upvote

thankyou !