An Introduction to Functional Programming Through Lambda Calculus

- 136 -(7::(APPEND (TRAVERSE EMPTY)(9::(TRAVERSE EMPTY)))) -> ... ->APPEND (APPEND (APPEND [](3::[]))(4::(APPEND [](5::[])))(7::(APPEND [](9::[]))) -> ... ->APPEND (APPEND [3](4::[5]))(7::[9]) -> ... ->APPEND [3,4,5] [7,9] -> ... ->[3,4,5,7,9]7.12. Binary tree searchOnce a binary tree has been constructed it may be searched to find out whether or not it contains a value. The searchalgorithm is very similar to the addition algorithm above. If the tree is empty then the search fails:TFIND V EMPTY = FALSEIf the tree is not empty, and the required value is the node value then the search succeeds:TFIND V (NODE NV L R) = TRUE if V NVOtherwise, if the requiredvalue comes before the node value then try the left branch:TFIND V (NODE NV L R) = TFIND V L if V NVOtherwise, try the right branch:TFIND V (NODE NV L R) = TFIND V R if NOT ( V NV)For example, for a binary integer tree:rec TFIND V EMPTY = ""or TFIND V [NV,L,R] =IF EQUAL V NVTHEN TRUEELSEIF LESS V NVTHEN TFIND V LELSE TFIND V RFor example:TFIND 5 [7,[4,[3,EMPTY,EMPTY],[5,EMPTY,EMPTY]],[9,EMPTY,EMPTY]] -> ... ->