/* 

  Ackermann Prolog style in Picat.

  For Picat version 3.0.

  This is a direct port of my SWI-Prolog model: http://hakank.org/swi_prolog/ackermann.pl

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


main => go.

go :-
        M = 3,
        between(0,10,N),
        writeln(n=N),
        % abolish_all_tables,
        time(once(a(M,N,R))),
        writeln([3,N,R]),
        fail,
        nl.
go.


% From
% https://groups.google.com/g/comp.lang.prolog/c/AX8plLWooJA
% Example expected result:
% 
% ?- depth(ack(3,4), 0, N).
% N = 10307.
go2 ?=>
  time(depth($ack(3,4), 0, N)),
  println(n=N),
  nl.
go2 => true.

table
a(0,N,A):- !,A is N+1.
a(M,0,A):- !,M1 is M-1, a(M1,1,A).
a(M,N,A):-
    M1 is M-1,
    N1 is N-1,
    a(M,N1,A1),
    a(M1,A1,A).


% https://groups.google.com/g/comp.lang.prolog/c/AX8plLWooJA
% (Jan Burse)
edge(ack(X, ack(Y, Z)), ack(X, H)) :- !, edge($ack(Y, Z), H).
edge(ack(0, N), X) :- !, X is N+1.
edge(ack(M, 0), ack(H, 1)) :- !, H is M-1.
edge(ack(M, N), ack(H, ack(M, J))) :- H is M-1, J is N-1.
 
depth(ack(X, Y), N, M) :- !,
  edge($ack(X, Y), H),
  J is N+1,
  depth(H, J, M).
  depth(_, N, N).