Part $5$ Positive Trees?

Implement the function

positive$-$trees?, which takes a list of trees and

returns #t if every member of the list is a positive tree, where a positive tree is

one whose numbers sum to a positive value.

Hint $1$: This function takes a list, not a tree, so don$$t try to use the template for

a tree function.

Hint $2$: Use your sum function as a helper.

Hint $3$: $($positive$-$trees? empty$)$ should produce #t$,$ because there$$s no tree in the

empty list whose numbers sum to $0$ or less.

More examples:

$($test $($positive$-$trees? $($cons $($leaf $6)$

empty$))$

#t$)$

$($test $($positive$-$trees? $($cons $($leaf $-6)$

empty$))$

#f$)$

$($test $($positive$-$trees? $($cons $($node $1($leaf $6)($leaf $-6))$

empty$))$

#t$)$

$($test $($positive$-$trees? $($cons $($node $1($leaf $6)($leaf $-6))$

$($cons $($node $0($leaf $0)($leaf $1))$

empty$)))$

#t$)$

$($test $($positive$-$trees? $($cons $($node $-1($leaf $6)($leaf $-6))$

$($cons $($node $0($leaf $0)($leaf $1))$

empty$)))$

#f$)$

Part $6-$Transmutation

Implement a

positive$-$thinking function, which takes a Tree as argument and produces

a new tree which removes all negative leaves from the original tree. If the

resulting tree would have no nodes, return false.

Hint: the total number of nodes $($leaf and interior$)$ in the resulting tree will be

less than or equal to the total number of nodes in the original, minus the number of

negative leaves in the original.