/* 

  Conditional probability in Picat.

  This is a port of my PSI model youtube5.wppl 
  (from a now unavailable YouTube video) 
  """
  def main() {
    x := uniform(0,1);
    d := infer((){
            y := uniform(0,1);
            observe(y <= x);
            return y;
         }) :Distribution[ℝ];
    r := sample(d);
    observe(x <= 1/2);

    return r;
  }
  """

  The (exact) expected value from PSI is E[r] = 1/8 (0.125)


  Cf my Gamble model gamble_youtube5.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 : r
  Probabilities (truncated):
  0.484143665285848: 0.0001000000000000
  0.48113154782035: 0.0001000000000000
  0.480283599570526: 0.0001000000000000
  0.479943752977971: 0.0001000000000000
  .........
  0.000056679360595: 0.0001000000000000
  0.000052151270235: 0.0001000000000000
  0.000029045157148: 0.0001000000000000
  0.000025116372865: 0.0001000000000000
  mean = 0.124932

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


% Using observe does not work.
sample1(X) = Res =>
  Y = uniform_dist(0,1),
  observe(Y <= X),
  if observed_ok then
    Res = Y
  end.

% However this works:
% Continue to draw Y until it's <= X
sample(X) = Res =>
  Y = uniform_dist(0,1),
  if (Y <= X)
    Res = Y
  else
    Res = sample(X)
  end.
  
model() =>
  X = uniform_dist(0,1),
  
  R = sample(X),
  observe(X <= 1/2),
  
  if observed_ok then
    add("r",R),    
  end.