/* 

  PPL in Picat.

  This is a port of my PSI model youtube6.wppl 
  (from a now unavailable YouTube video) 
  """
  def main() {
    x := uniform(0,1);
    y := uniform(0,1);
    // z := y - 2*x; // 𝔼[x] = 1/4
    // cobserve(z,0);   
    z := y/x;  // 𝔼[x] = 1/4
    cobserve(z,2);
  
    return  x;
  }
  """

  The (exact) expected value from PSI is E[x] = 1/3 (0.3333)

  Cf my Gamble model gamble_youtube6.rkt

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

*/

import ppl_distributions, ppl_utils.
import util.

main => go.

/*

  var : x
  Probabilities (truncated):
  0.525951048138529: 0.0001000000000000
  0.525374848174571: 0.0001000000000000
  0.524806940241161: 0.0001000000000000
  0.524341818189408: 0.0001000000000000
  .........
  0.006926609672106: 0.0001000000000000
  0.006104269999128: 0.0001000000000000
  0.004969122356255: 0.0001000000000000
  0.003065420781758: 0.0001000000000000
  mean = 0.335194

  var : y
  Probabilities (truncated):
  0.999886195640958: 0.0001000000000000
  0.999858767725462: 0.0001000000000000
  0.999838099349215: 0.0001000000000000
  0.999831553548496: 0.0001000000000000
  .........
  0.013509441639068: 0.0001000000000000
  0.012532647239292: 0.0001000000000000
  0.010166814555492: 0.0001000000000000
  0.006299870557291: 0.0001000000000000
  mean = 0.668598

  var : z
  Probabilities (truncated):
  2.099983690497761: 0.0001000000000000
  2.09993300104227: 0.0001000000000000
  2.099926465809096: 0.0001000000000000
  2.099886348427928: 0.0001000000000000
  .........
  1.900119742327797: 0.0001000000000000
  1.900084010604907: 0.0001000000000000
  1.900078498904452: 0.0001000000000000
  1.900044464391844: 0.0001000000000000
  mean = 1.99628


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,min_accepted_samples=10000,show_accepted_samples=true]),
  nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  X = uniform(0,1),
  Y = uniform(0,1),

  Z = Y / X,
  observe(abs(Z-2.0) < 0.1),
  
  if observed_ok then
    add("x",X),
    add("y",Y),
    add("z",Z),
  end.