// Tower of Hanoi Puzzle

// Rules
hanoi(return, source, target, aux) >< Z => 
          // Erase the source, target and aux
          source ~ Eraser,
          target ~ Eraser,
          aux ~ Eraser,

          // result
          return~[];

hanoi(return, source, target, aux) >< S(n) => 
          // Duplicate the source, target and aux
	  source ~ Dup(src1, Dup(src2, src3)),
          target ~ Dup(tgt1, Dup(tgt2, tgt3)),
          aux ~ Dup(aux1, aux2),

	  
          // recursive applications
	  n ~ Dup(nn1, Dup(nn2, nn3)),
          hanoi(ret1, src1, aux1, tgt1)~nn1,
          hanoi(ret2, aux2, tgt2, src2)~nn2,

          // result
	  append(return, ((nn3,src3,tgt3)):ret2)~ret1;


// ---------------------------------------
// append
// ---------------------------------------
append(r,a) >< [] => r~a;
append(r,a) >< x:xs => r~x:w, append(w,a)~xs;


// ---------------------------------------
// len
// ---------------------------------------
len(ret) >< [] => ret~Z;
len(ret) >< x:xs => len_(ret, S(Z))~xs, Eraser~x;
len_(ret, n) >< [] => ret~n;
len_(ret, n) >< x:xs => len_(ret, S(n))~xs, Eraser~x;



// Net
hanoi(result, A, C, B) ~
//1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
  S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(S(Z))))))))))))))))))),

len(r)~result;
prnat r;