/* 

  Perfect number benchmark in Picat.

  From 
  http://www.jekejeke.ch/idatab/doclet/prod/en/docs/05_run/15_stdy/06_bench/09_programs/10_perfect/01_perfect.p.html

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

*/


% import util.
% import cp.


main => go.


/**
 * Prolog code for finding a perfect number.
 *
 * A solution that did not make use of findall/3 and rem/2 
 * was posted Dec 16, 1988 on comp.lang.prolog by Thomas 
 * Sj|land. It was titled Christmas pleasure and contained
 * an invitation to further dig into Euclids theorem.

 */


between1(Lo,Hi,_), Lo>Hi => fail.
between1(Lo,_Hi,X) ?=> X = Lo.
between1(Lo,Hi,X) => Lo2 = Lo+1, between1(Lo2,Hi,X).

sumlist1([],S) => S = 0.
sumlist1([X|Y],R) => sumlist1(Y,H), R = X+H.

perfect(Hi,X) =>
    between1(1,Hi,X),
    % between(1,Hi,X),
    Y = X // 2,
    % L = findall(Z,$(between1(1,Y,Z), (X rem Z == 0))),
    L = [Z : Z in 1..Y, X rem Z == 0],
    %writeln(l=L),
    sumlist1(L,X).

perfect =>
    perfect(500,P),
    writeln(P).

perfect2 =>
    perfect(500,_P).



go => perfect.

go2 => perfect2.