Follow the instruction given below and provide the two dafny functions that behave in the same manner as that of the Ocaml code given.

You are given the following Dafny datatype, which is equivalent

to the following OCaml tree type:

$/*$ type 'a tree $=$ Leaf $|$ Node of $(\text{'}$a $*$ 'a tree $**$ 'a tree$)*/$

datatype Tree $=$

$|$ Leaf

$|$ Node $($data:T$,$ left: Tree, right:Tree$)$

$/*$ Implement the $`$map$`$ and $`$fold$`$ functions over these trees.

For reference, the OCaml definition would be:

let rec mapTree f t $=$

match t with

$|$ Leaf $->$ Leaf

$|$ Node $($x$,$l$,$r$)->$ Node $($f x$,$ mapTree f l$,$ mapTree f r$)$

let rec foldTree f e t $=$

match t with

$|$ Leaf $->$ e

$|$ Node $($x$,$l$,$r$)->$ f x $($foldTree f e l$)($foldTree f e r$)$

$*/$

Here is the skeleton for map:

function mapTree $($f: A $->$ B$,$ t: Tree$)$: Tree $\{$

$//$ Replace with your implementation

Leaf

$\}$

Make a fold function $($in dafny$)$ with the same argument order as the Ocaml code.