Rosetta example:https://rosettacode.org/wiki/Tree_traversal

Implement a binary tree structure, with each node carrying an integer as a node label, and four traversal strategies: pre-order, in-order, postorder, and levelorder traversals.

https://rosettacode.org/wiki/Tree_traversal

package req nx

The class Tree implements the basic binary composite structure (left, right).

nx::Class create Tree {
    :property -accessor public value:required
    :property -accessor public left:object,type=[current]
    :property -accessor public right:object,type=[current]

    :public method traverse {order} {
        set list {}
        :$order v {
            lappend list $v
        }
        return $list
    }

    # Traversal methods
    :public method preOrder {varName script {level 0}} {
        upvar [incr level] $varName var
        set var ${:value}
        uplevel $level $script
        if {[info exists :left]} {${:left} preOrder $varName $script $level}
        if {[info exists :right]} {${:right} preOrder $varName $script $level}
    }

    :public method inOrder {varName script {level 0}} {
        upvar [incr level] $varName var
        if {[info exists :left]} {${:left} inOrder $varName $script $level}
        set var ${:value}
        uplevel $level $script
        if {[info exists :right]} {${:right} inOrder $varName $script $level}
    }
    :public method postOrder {varName script {level 0}} {
        upvar [incr level] $varName var
        if {[info exists :left]} {${:left} postOrder $varName $script $level}
        if {[info exists :right]} {${:right} postOrder $varName $script $level}
        set var ${:value}
        uplevel $level $script
    }
    :public method levelOrder {varName script} {
        upvar 1 $varName var
        set nodes [list [current]]
        while {[llength $nodes] > 0} {
            set nodes [lassign $nodes n]
            set var [$n value get]
            uplevel 1 $script
            if {[$n eval {info exists :left}]} {lappend nodes [$n left get]}
            if {[$n eval {info exists :right}]} {lappend nodes [$n right get]}
        }
    }
}

This is a factory method to build up the object tree recursively from a nested Tcl list. Note that we create left and right children by nesting them in their parent, this provides for a cascading cleanup of an entire tree (there is no need for an explicit cascading of destroy methods down the composite).

Tree public object method newFromList {-parent l} {
    lassign $l value left right
    set n [:new {*}[expr {[info exists parent]?[list -childof $parent]:""}] -value $value]
    set props [list]
    if {$left ne ""} {lappend props -left [:newFromList -parent $n $left]}
    if {$right ne ""} {lappend props -right [:newFromList -parent $n $right]}
    $n configure {*}$props
    return $n
}

Run the required tests:

set t [Tree newFromList {1 {2 {4 7} 5} {3 {6 8 9}}}]
% $t traverse preOrder
1 2 4 7 5 3 6 8 9
% $t traverse inOrder
7 4 2 5 1 8 6 9 3
% $t traverse postOrder
7 4 5 2 8 9 6 3 1
% $t traverse levelOrder
1 2 3 4 5 6 7 8 9