1:- module(
    2  tree,
    3  [
    4    depth/2,   % +Tree, ?Depth
    5    shortest/2 % +Trees, ?Tree
    6  ]
    7).

tree(leaf, 'Electra', [])

tree(father,
     'Agamemnon',
     [tree(leaf, 'Electra', []),
      tree(leaf, 'Orestes', [])])

tree('Modus ponens',
     'Socrates is mortal',
     [tree(premise, 'Sorcrates is a man', []),
      tree(premise, 'Men are mortal', [])])

   40:- use_module(library(aggregate)).   41:- use_module(library(lists)).

 depth(+Tree:compound, +Depth:nonneg) is semidet

depth(+Tree:compound, -Depth:nonneg) is det

Succeeds for the Depth of the Tree.

The depth of a tree is defined inductively:

• 0 for leaf nodes.
• 1 plus the maxium of the depth of the children.

   54depth(tree(_,_,[]), 0).
   55depth(tree(_,_,Trees), Depth) :-
   56  aggregate_all(
   57    max(Depth),
   58    (
   59      member(Tree, Trees),
   60      depth(Tree, Depth)
   61    ),
   62    Depth
   63  ).

 shortest(+Trees:list(compound), +Tree:compound) is semidet

shortest(+Trees:list(compound), -Tree:compound) is det

Succeeds if Tree is the shotests of Trees.

   72shortest(Trees, Tree) :-
   73  aggregate_all(
   74    min(Depth0,Tree0),
   75    (
   76      member(Tree0, Trees),
   77      depth(Tree0, Depth0)
   78    ),
   79    min(_, Tree)
   80  )