/* 

  Battalion in Picat.

  "First-Order Probabilistic Inference"
  https://www.youtube.com/watch?v=leIqVD4-Fks
  Time 45:06
   
  (The shown model in the talks is a BLOG model).

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

/*

  var : large(1)
  Probabilities:
  true: 0.5965000000000000
  false: 0.4035000000000000
  mean = [true = 0.5965,false = 0.4035]

  var : num-battalion
  Probabilities:
  1: 0.1120000000000000
  5: 0.1085000000000000
  10: 0.1040000000000000
  6: 0.1020000000000000
  2: 0.1010000000000000
  3: 0.0995000000000000
  9: 0.0970000000000000
  8: 0.0930000000000000
  7: 0.0930000000000000
  4: 0.0900000000000000
  mean = 5.435

  var : num_soldier(1)
  Probabilities (truncated):
  300: 0.0330000000000000
  737: 0.0140000000000000
  748: 0.0135000000000000
  740: 0.0130000000000000
  733: 0.0125000000000000
  745: 0.0105000000000000
  727: 0.0105000000000000
  749: 0.0100000000000000
  742: 0.0100000000000000
  734: 0.0100000000000000
  763: 0.0095000000000000
  738: 0.0095000000000000
  730: 0.0090000000000000
  759: 0.0085000000000000
  753: 0.0085000000000000
  752: 0.0085000000000000
  741: 0.0085000000000000
  739: 0.0085000000000000
  736: 0.0085000000000000
  717: 0.0085000000000000
  .........
  673: 0.0005000000000000
  669: 0.0005000000000000
  596: 0.0005000000000000
  579: 0.0005000000000000
  566: 0.0005000000000000
  558: 0.0005000000000000
  557: 0.0005000000000000
  550: 0.0005000000000000
  549: 0.0005000000000000
  545: 0.0005000000000000
  544: 0.0005000000000000
  538: 0.0005000000000000
  478: 0.0005000000000000
  459: 0.0005000000000000
  457: 0.0005000000000000
  453: 0.0005000000000000
  452: 0.0005000000000000
  450: 0.0005000000000000
  443: 0.0005000000000000
  431: 0.0005000000000000

  mean = 644.24

  var : num_soldiers_per-battalion
  Probabilities (truncated):
  [300]: 0.0145000000000000
  [766]: 0.0025000000000000
  [511]: 0.0025000000000000
  [759]: 0.0020000000000000
  [744]: 0.0020000000000000
  [729]: 0.0020000000000000
  [765]: 0.0015000000000000
  [758]: 0.0015000000000000
  [751]: 0.0015000000000000
  [740]: 0.0015000000000000
  [736]: 0.0015000000000000
  [730]: 0.0015000000000000
  [708]: 0.0015000000000000
  [700]: 0.0015000000000000
  [515]: 0.0015000000000000
  [512]: 0.0015000000000000
  [300,300]: 0.0015000000000000
  [792]: 0.0010000000000000
  [789]: 0.0010000000000000
  [782]: 0.0010000000000000
  .........
  [300,726,683]: 0.0005000000000000
  [300,725,496,759,699,737,775]: 0.0005000000000000
  [300,720]: 0.0005000000000000
  [300,717]: 0.0005000000000000
  [300,530]: 0.0005000000000000
  [300,529]: 0.0005000000000000
  [300,528]: 0.0005000000000000
  [300,527,735]: 0.0005000000000000
  [300,526,511,488]: 0.0005000000000000
  [300,524,491,508]: 0.0005000000000000
  [300,523,715,751,747,726,739]: 0.0005000000000000
  [300,506]: 0.0005000000000000
  [300,503]: 0.0005000000000000
  [300,501,761]: 0.0005000000000000
  [300,501,559]: 0.0005000000000000
  [300,480]: 0.0005000000000000
  [300,473]: 0.0005000000000000
  [300,471,464,513]: 0.0005000000000000
  [300,470,828,777]: 0.0005000000000000
  [300,461,746,488]: 0.0005000000000000

  Mean (truncated)
  mean = [[300] = 0.0145,[766] = 0.0025,[511] = 0.0025,[759] = 0.002,[744] = 0.002,[729] = 0.002,[765] = 0.0015,[758] = 0.0015,[751] = 0.0015,[740] = 0.0015,[736] = 0.0015,[730] = 0.0015,[708] = 0.0015,[700] = 0.0015,[515] = 0.0015,[512] = 0.0015,[300,300] = 0.0015,[792] = 0.001,[789] = 0.001,[782] = 0.001]

  var : region(1)
  Probabilities:
  2: 0.1150000000000000
  6: 0.0995000000000000
  3: 0.0960000000000000
  5: 0.0950000000000000
  7: 0.0885000000000000
  4: 0.0880000000000000
  8: 0.0775000000000000
  9: 0.0685000000000000
  10: 0.0575000000000000
  1: 0.0565000000000000
  11: 0.0465000000000000
  12: 0.0365000000000000
  13: 0.0305000000000000
  14: 0.0180000000000000
  15: 0.0125000000000000
  16: 0.0070000000000000
  17: 0.0045000000000000
  19: 0.0010000000000000
  18: 0.0010000000000000
  21: 0.0005000000000000
  mean = 6.451

*/
go ?=>
  reset_store(),
  run_model(2000,$model,[show_probs_trunc,mean,truncate_size=20]),
  fail,  
  nl.
go => true.
  

large(Bat) = flip(0.6).
region(Bat,NumBattalion) = 1 + poisson_dist(NumBattalion).
num_soldier(Bat,LargeBat,NumBattalion) = cond( LargeBat == true, poisson_dist(1500),
                                 cond( region(Bat,NumBattalion) == 2, 300, poisson_dist(500))).
model() =>
  NumBattalion = random_integer1(10),
  NumSoldiersPerBattalion = [num_soldier(Bat,large(Bat),NumBattalion)  : Bat in 1..NumBattalion],
  add("num-battalion", NumBattalion),
  add("large(1)", large(1)),
  add("region(1)",region(1,NumBattalion)),
  add("num_soldier(1)",num_soldier(1,large(1),NumBattalion)),
  add("num_soldiers_per-battalion",NumSoldiersPerBattalion).