An Introduction to Functional Programming Through Lambda Calculus

- 134 -[7,[4,[3,EMPTY,EMPTY],EMPTY],[9,EMPTY,EMPTY]]To add 5 to this tree:TADD 5 [7,[4,[3,EMPTY,EMPTY],EMPTY],[9,EMPTY,EMPTY]]5 comes before 7 so it is added to the left sub-tree:[7,(TADD 5 [4,[3,EMPTY,EMPTY],EMPTY]),[9,EMPTY,EMPTY]]Now, 5 comes after 4 so it is added to the right sub-tree:[7,[4,[3,EMPTY,EMPTY],(TADD 5 EMPTY)],[9,EMPTY,EMPTY]] -> ... ->[7,[4,[3,EMPTY,EMPTY],[5,EMPTY,EMPTY]],[9,EMPTY,EMPTY]]To add an arbitrary list of numbers to a tree, if the list is empty then return the tree. Otherwise add the tail of the list tothe result of adding the head of the list to the tree:Thus:rec TADDLIST [] TREE = TREEor TADDLIST (H::T) TREE = TADDLIST T (TADD H TREE)TADDLIST [7,4,9,3,5,11,6,8] EMPTY -> ... ->[7,[4,