/* 

  Schelling coordination game in Picat.

  This is a port of the Church ForestDB model, http://forestdb.org/models/schelling.html

  Here we also study different priors for selecting the good bar (over the bad bar).

  Cf my Gamble model gamble_schelling_coordination_game.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.

/*
   Using different priors for the good bar and different recursion depths.

   prior = 0.6
   [p = 0.6,depth = 1]
   var : location
   Probabilities:
   good_bar: 0.7753232758620690
   bad_bar: 0.2246767241379310


   Variable lengths:
   location = 11136

   [p = 0.6,depth = 2]
   var : location
   Probabilities:
   good_bar: 0.8851556045166621
   bad_bar: 0.1148443954833379


   Variable lengths:
   location = 3631

   [p = 0.6,depth = 3]
   var : location
   Probabilities:
   good_bar: 0.9349736379613357
   bad_bar: 0.0650263620386643


   Variable lengths:
   location = 1138

   [p = 0.6,depth = 4]
   var : location
   Probabilities:
   good_bar: 0.9872773536895675
   bad_bar: 0.0127226463104326


   Variable lengths:
   location = 393

   [p = 0.6,depth = 5]
   var : location
   Probabilities:
   good_bar: 0.9907407407407407
   bad_bar: 0.0092592592592593


   Variable lengths:
   location = 108

   [p = 0.6,depth = 6]
   var : location
   Probabilities:
   good_bar: 1.0000000000000000


   Variable lengths:
   location = 62

   prior = 0.51
   [p = 0.51,depth = 1]
   var : location
   Probabilities:
   good_bar: 0.5296926290659505
   bad_bar: 0.4703073709340496


   Variable lengths:
   location = 10053

   [p = 0.51,depth = 2]
   var : location
   Probabilities:
   good_bar: 0.5502218636546995
   bad_bar: 0.4497781363453005


   Variable lengths:
   location = 2479

   [p = 0.51,depth = 3]
   var : location
   Probabilities:
   good_bar: 0.5915492957746479
   bad_bar: 0.4084507042253521


   Variable lengths:
   location = 639

   [p = 0.51,depth = 4]
   var : location
   Probabilities:
   good_bar: 0.6047904191616766
   bad_bar: 0.3952095808383234


   Variable lengths:
   location = 167

   [p = 0.51,depth = 5]
   var : location
   Probabilities:
   good_bar: 0.7647058823529411
   bad_bar: 0.2352941176470588


   Variable lengths:
   location = 34

   [p = 0.51,depth = 6]
   var : location
   Probabilities:
   good_bar: 0.8000000000000000
   bad_bar: 0.2000000000000000


   Variable lengths:
   location = 5

   prior = 0.5
   [p = 0.5,depth = 1]
   var : location
   Probabilities:
   good_bar: 0.5043107820265748
   bad_bar: 0.4956892179734253


   Variable lengths:
   location = 9859

   [p = 0.5,depth = 2]
   var : location
   Probabilities:
   bad_bar: 0.5001964636542240
   good_bar: 0.4998035363457760


   Variable lengths:
   location = 2545

   [p = 0.5,depth = 3]
   var : location
   Probabilities:
   good_bar: 0.5253968253968254
   bad_bar: 0.4746031746031746


   Variable lengths:
   location = 630

   [p = 0.5,depth = 4]
   var : location
   Probabilities:
   bad_bar: 0.5472972972972973
   good_bar: 0.4527027027027027


   Variable lengths:
   location = 148

   [p = 0.5,depth = 5]
   var : location
   Probabilities:
   good_bar: 0.5581395348837209
   bad_bar: 0.4418604651162791


   Variable lengths:
   location = 43

   [p = 0.5,depth = 6]
   var : location
   Probabilities:
   bad_bar: 0.6250000000000000
   good_bar: 0.3750000000000000


   Variable lengths:
   location = 8


   prior = 0.4
   [p = 0.4,depth = 1]
   var : location
   Probabilities:
   bad_bar: 0.7705035971223022
   good_bar: 0.2294964028776978


   Variable lengths:
   location = 11120

   [p = 0.4,depth = 2]
   var : location
   Probabilities:
   bad_bar: 0.8818000569638280
   good_bar: 0.1181999430361720


   Variable lengths:
   location = 3511

   [p = 0.4,depth = 3]
   var : location
   Probabilities:
   bad_bar: 0.9486963835155593
   good_bar: 0.0513036164844407


   Variable lengths:
   location = 1189

   [p = 0.4,depth = 4]
   var : location
   Probabilities:
   bad_bar: 0.9913978494623656
   good_bar: 0.0086021505376344


   Variable lengths:
   location = 465

   [p = 0.4,depth = 5]
   var : location
   Probabilities:
   bad_bar: 0.9815950920245399
   good_bar: 0.0184049079754601


   Variable lengths:
   location = 163

   [p = 0.4,depth = 6]
   var : location
   Probabilities:
   bad_bar: 0.9818181818181818
   good_bar: 0.0181818181818182


   Variable lengths:
   location = 55


*/
go ?=>
  member(P,[0.6,0.51,0.5,0.4]),
  println(prior=P),
  
  member(Depth,1..6),
  println([p=P,depth=Depth]),
  reset_store,
  run_model(40_000,$model(P,Depth),[show_probs]), % [show_probs,min_accepted_samples=1000]),
  nl,
  show_store_lengths,nl,
  fail,
  nl.
go => true.


% This was the original problem, i.e. prior of 0.6
% sample_location() = cond(flip(0.6) == true,good_bar,bad_bar).

% Let's generalize this for various priors of good bar
sample_location(P) = cond(flip(P) == true, good_bar, bad_bar).


% Alice think about what Bob think about what Alice think what Bob think...
alice(Depth,P) = Res =>
  AliceLocation = sample_location(P),
  observe(AliceLocation == bob(Depth-1,P)),
  Res = AliceLocation.

% Bob think about what Alice think what Bob think...
bob(Depth,P) = Res =>
  BobLocation = sample_location(P),
  if Depth == 0 then
    observe(true)
  else
    observe(BobLocation == alice(Depth,P))
  end,
  Res = BobLocation.
  
model(P,Depth) =>
  Location = bob(Depth,P),
    
  if observed_ok then
    add("location",Location)
  end.