/* 

  Car in box in Picat.

  From https://medium.com/puzzle-sphere/can-you-find-the-right-box-d01521f17015
  """
  There are 3 boxes, exactly one of which has a car. You can keep the car 
  if you pick the correct box!

  On each box, there is a statement, exactly one of which is true.

  - Box 1: The car is in this box.
  - Box 2: The car is not in this box.
  - Box 3: The car is not in box 1.

  Which box has the car?
  """


  Cf  
  - CP model car_in_box.pi
  - my Gamble model gamble_car_in_box.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.
% import ordset.

main => go.

/*

  Num accepted samples: 1000  Total samples: 22641  (0.044%)

  var : car
  Probabilities:
  2: 1.0000000000000000
  mean = 2.0

  var : boxes
  Probabilities:
  [0,0,1]: 1.0000000000000000
  mean = [[0,0,1] = 1.0]


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % show_histogram,
                           min_accepted_samples=1000,show_accepted_samples=false
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.

  
model() =>
  N = 3,
  Car = random_integer1(N),
  % Boxes = uniform_draw_n([0,1],N),
  % observe(Boxes.sum == 1),
  Boxes = uniform_draw([[0,0,1],[0,1,0],[1,0,0]]),

  % Box 1: The car is in this box.
  equivalence(Boxes[1] == 1,Car == 1),
  
  % Box 2: The car is not in this box.
  equivalence(Boxes[2] == 1,Car != 2),
  
  % Box 3: The car is not in box 1.
  equivalence(Boxes[3] == 1,Car != 1),
  
  if observed_ok then
    add("car",Car),
    add("boxes",Boxes),    
  end.