An Introduction to Functional Programming Through Lambda Calculus

- 219 -λb.b3)i) a) (identity ) => ... =>b) ((apply (apply identity)) ) => ... =>((apply identity) ) => ... =>(identity ) => ... =>ii) a) ((apply ) ) => ... =>( )b) ((λx.λy.(((make_pair x) y) identity) ) ) =>(λy.(((make_pair ) y) identity) ) =>(((make_pair ) ) identity) => ... =>((identity ) ) => ... =>( )iii) a) (identity ) => ... =>b) ((self_apply (self_apply select_second)) ) => ... =>(((self_apply select_second) (self_apply select_second))) => ... =>(((select_second select_second) (select_second select_second))) => ... =>((λsecond.second (select_second select_second) ) => ... =>((select_second select_second) ) => ... =>(λsecond.second ) =>4)def make_triplet = λfirst.λsecond.λthird.λs.(((s first) second) third)def triplet_first = λfirst.λsecond.λthird.firstdef triplet_second = λfirst.λsecond.λthird.seconddef triplet_third = λfirst.λsecond.λthird.thirdmake_triplet triplet_first ==λfirst.λsecond.λthird.λs.(((s first) second) third) triplet_first => ... =>(((triplet_first ) ) ) ==(((λfirst.λsecond.λthird.first ) ) ) => ... =>