Define a polymorphic Tree data type, where a Tree is either a Node with a left subtree, a value, and a right subtree; or it is Null.

Also define a companion object for the Tree data type, with the following functions:

$($a$)$ Three polymorphic functions $--$ inOrder, preOrder, and postOrder $--$ to traverse the tree in$-$order, pre$-$order, and post$-$order. Each function takes a tree and returns a list with the contents of the tree when traversed in that order.

$($b$)$ A polymorphic function, search, which takes two arguments $$ a Tree and a key $$ and returns a boolean result based on whether the key is found in the tree.

$($c$)$ A polymorphic function, replace, which takes three arguments $$ a Tree t$,$ a value before, and a value after $$ and returns t with ALL instances of before replaced with the value after.

$[$Hint: Model your Tree data type after the List data type.$]$