Generalized Verbal Arithmetic in Prolog.

verbalArithmetic.pl

pad(W1, W2, X, Y) :-
  length(W1, L1),
  length(W2, L2),
  padZero(W1, W2, L1, L2, X, Y).

padZero(W1, W2, L, L, [0|W1], [0|W2]).
padZero(W1, W2, L1, L2, X, Y) :- L1 #> L2, pad(W1, [0|W2], X, Y).
padZero(W1, W2, L1, L2, X, Y) :- L1 #< L2, padZero(W2, W1, L2, L1, Y, X).

stripZero([], []).
stripZero([0|T], T).
stripZero([H|T], [H|T]) :- H #> 0.

sum([], [], [], 0, 0).
sum([H1|T1], [H2|T2], [H3|T3], C1, C2) :-
  sum(T1, T2, T3, C2, _),
  H3 #= (H1 + H2 + C2) rem 10,
  C1 #= (H1 + H2 + C2) // 10.

verbalArithmetic([], [], [], []).
verbalArithmetic(V, [H1|W1], [H2|W2], [H3|W3]) :-
  fd_domain(V, 0, 9),
  fd_all_different(V),
  H1 #\= 0, H2 #\= 0, H3 #\= 0,
  pad([H1|W1], [H2|W2], X, Y),
  sum(X, Y, Z, _, _),
  stripZero(Z, [H3|W3]),
  fd_labeling(V).