An Introduction to Functional Programming Through Lambda Calculus

- 98 -This leads naturally to:NIL = []which is a list of no objects with an implicit NIL at the end.For example, a list of pairs:CONS (CONS 5 (CONS 12 NIL))(CONS (CONS 10 (CONS 15 NIL))(CONS (CONS 15 (CONS 23 NIL))(CONS (CONS 20 (CONS 45 NIL))NIL)))becomes the compact:[[5,12],[10,15],[15,23],[20,45]]As before, HEAD selects the head element:HEAD (X::Y) = XHEAD [X,L] = XFor example:HEAD [[5,12],[10,15],[15,23],[20,45]] => ... =>[5,12]and TAIL selects the tail:TAIL (X::Y) = YTAIL [X,L] = [L]for example:and:TAIL [[5,12],[10,15],[15,23],[20,45]] => ... =>[[10,15],[15,23],[20,45]]TAIL [5] => ... =>[]Note that constructing a list with CONS is not the same as using [ and ]. For lists constructed with [ and ] there isan assumed empty list at the end. Thus:[,] ==CONS (CONS NIL)We may simplify long lists made from :: by dropping intervening brackets. Thus:::(::) ==::::