/* 

  Where is my bag? in Picat.

  From "Probabilistic Reasoning Under Uncertainty with Bayesian Networks"
  https://www.bayesia.com/2018-03-02-probabilistic-reasoning-under-uncertainty

  (Also see The BaysiaLabBook "Bayesian Networks BayesiaLab" v1, page 51f.)

  Travel from Singapore -> Tokyo -> Los Angeles.
  1) The departure of Singapore -> Tokyo is delayed
  2) Just made the Tokyo -> LA trip. There's a 50/50 change the luggage is on the plane to LA.
  3) Arriving at LA, waiting for the luggage in 5 minutes, the luggage has not been seen.
  What is the probability that the bag was in the Tokyo -> LA plane?
  
  Answer: The probability that the bag was with the LA plane is 33% (as in the talk).
  From Judea Pearl: The Book of Why.


  Exact probabilities from my Gamble model:

  (bag-on-plane-p 1/2 wait-time 5)
  (#f : 2/3 (0.6666666666666666))
  (#t : 1/3 (0.3333333333333333))


  (bag-on-plane-p 1/2 wait-time 8)
  (#f : 5/6 (0.8333333333333334))
  (#t : 1/6 (0.16666666666666666))


  (bag-on-plane-p 4/5 wait-time 5)
  (#t : 2/3 (0.6666666666666666))
  (#f : 1/3 (0.3333333333333333))


  (bag-on-plane-p 4/5 wait-time 8)
  (#f : 5/9 (0.5555555555555556))
  (#t : 4/9 (0.4444444444444444))


  This is a port of my Racket/Gamble model gamble_where_is_my_bag.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.

main => go.

/*
  [bag_on_plane_p = 0.5,wait_time = 5]
  var : bag on the plane
  Probabilities:
  false: 0.65889735544598838 (1470 / 2231)
  true: 0.34110264455401168 (761 / 2231)

  [bag_on_plane_p = 0.5,wait_time = 8]
  var : bag on the plane
  Probabilities:
  false: 0.82537067545304776 (501 / 607)
  true: 0.17462932454695224 (106 / 607)

  [bag_on_plane_p = 0.8,wait_time = 5]
  var : bag on the plane
  Probabilities:
  true: 0.66647887323943666 (1183 / 1775)
  false: 0.33352112676056339 (592 / 1775)

  [bag_on_plane_p = 0.8,wait_time = 8]
  var : bag on the plane
  Probabilities:
  false: 0.57212003872216843 (591 / 1033)
  true: 0.42787996127783157 (442 / 1033)

*/
go ?=>
  member([BagOnPlaneP,WaitTime], [[1/2,5],
                                  [1/2,8],
                                  [8/10,5],
                                  [8/10,8]
                                 ]),
  println([bag_on_plane_p=BagOnPlaneP,wait_time=WaitTime]),
  reset_store,
  run_model(30_000,$model(BagOnPlaneP,WaitTime),[show_probs_rat]),
  fail,
  nl.
go => true.


model(BagOnPlaneP,WaitTime) =>
  MaxTime = 10,
  
  % We know that the bag was on the plane with 50% probability.
  % Variant: https://www.youtube.com/watch?v=c71pnonOMkI&t=1074s it's 80/20.
  BagOnPlane = flip(BagOnPlaneP),
       
  % We assume uniform time step
  TTime = random_integer(MaxTime), % 0..MaxTime-1
    
  % Probability that the bag is on the carousel given a specific time
  % (if it was on the plane, that is).
  % The probability that the bag is on the carousel on a given time
  % is directly proportional on the time:
  %     time / maxTime
  BagOnCarousel = cond(BagOnPlane == true, flip(TTime / MaxTime), false),
    
  % He waited 5 minutes without seeing the luggage.
  % Is the bag on the plane?
  % add("bag on the carousel",BagOnCarousel),
  % add("t-time",TTime),
  observe(TTime == WaitTime, BagOnCarousel == false),

  if observed_ok  then
    add("bag on the plane",BagOnPlane),  
    % add("p",1)
  else
    true
    % add("p",0)
  end.