`Tree`¶

Tree[data, {children…}] is a tree node; None in place of the children makes a leaf. The data and the children are read back with TreeData and TreeChildren:

$ wo 't = Tree[1, {Tree[2, None], Tree[3, None]}]; {TreeData[t], Length[TreeChildren[t]]}'
{1, 2}

TreeLeaves gives the leaf subtrees, left to right:

$ wo 'TreeLeaves[Tree[1, {Tree[2, {Tree[4, None]}], Tree[3, None]}]]'
{Tree[4, None], Tree[3, None]}

TreeCases gives the subtrees whose data matches, children before their parent, and TreeScan visits them in that same order:

$ wo 'TreeCases[Tree[1, {Tree[2, {Tree[4, None]}], Tree[3, None]}], _?EvenQ]'
{Tree[4, None], Tree[2, {Tree[4, None]}]}

$ wo 'Reap[TreeScan[Sow, Tree[1, {Tree[2, {Tree[4, None]}], Tree[3, None]}]]]'
{Null, {{4, 2, 3, 1}}}

A tree is an atom: it has no parts, no depth beyond itself, and counts as a single leaf — so Map and Apply leave it alone:

$ wo '{AtomQ[Tree[1, None]], Depth[Tree[1, {Tree[2, None]}]], Length[Tree[1, None]], LeafCount[Tree[1, {Tree[2, None]}]]}'
{True, 1, 0, 1}

$ wo 'Map[f, Tree[1, {Tree[2, None]}]]'
Tree[1, {Tree[2, None]}]

Tree¶

`Tree`¶