Reversible tree length relation

Question

I\'m trying to write reversible relations in \"pure\" Prolog (no is, cut, or similar stuff. Yes it\'s homework), and I must admit I don\'t have a clue how. I do

Answer 1

Interesting problem.

Here's what I would do. Basically, your relation isn't reversible since add/3 isn't. What I essentially did was, replace counting with numbers with counting with lists of a size that corresponds to the number of leaves - which is reversible (well, append/3 and length/2 are reversible).

Is this something like what you need? The posted code is runnable under YAP.

PS: this might not be the most concise solution, but it's from the top of my head. I'll try to help if you have any further questions.

:-  use_module(library(lists)).

do_tree_len(n(_,leaf,leaf), [X]).
do_tree_len(n(op,G,D), [X1,X2|T]) :-
    append(TG, TD, [X1,X2|T]),
    TG \= [X1,X2|T], % To prevent infinite loops, when TG or TD is []
    TD \= [X1,X2|T],
    do_tree_len(G, TG),
    do_tree_len(D, TD).

tree_len(Tree, N):-
    length(L, N),
    do_tree_len(Tree, L).