/* 

  Orchs problem in Picat.

  From https://cbmm.mit.edu/sites/default/files/documents/CBMM_Church_Notes.html

  Here are some of The Battle of the Two Towers Church models (a few of them
  just uses variant Church method which is not supported by Picat PPL and
  are thus ignored).
  

  Cf
  - ppl_orchs.pi 
  - my Gamble model gamble_orchs_church.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.

/*

  * Problem 1
    """
    You are studying the historical Battle of the Two Towers. Suppose a-priori
    you assume Legolas, Gimli and Eowyn each took out somewhere between 0 and 19 orcs.
    How many orcs did Gimli take out?
    """

    var : gimli
    Probabilities:
    19: 0.0537000000000000
    2: 0.0529000000000000
    17: 0.0528000000000000
    4: 0.0528000000000000
    12: 0.0526000000000000
    18: 0.0522000000000000
    6: 0.0518000000000000
    0: 0.0505000000000000
    1: 0.0502000000000000
    10: 0.0498000000000000
    13: 0.0496000000000000
    3: 0.0493000000000000
    11: 0.0488000000000000
    5: 0.0486000000000000
    9: 0.0484000000000000
    14: 0.0480000000000000
    15: 0.0476000000000000
    16: 0.0474000000000000
    8: 0.0465000000000000
    7: 0.0465000000000000
    mean = 9.5147


  * Problem 2
    """
    Someone tells you that together, they took out at least 45 orcs. What is
    your belief about how many orcs Gimli took out?
    """

    var : gimli
    Probabilities:
    19: 0.1980000000000000
    18: 0.1660000000000000
    17: 0.1590000000000000
    16: 0.1130000000000000
    15: 0.1080000000000000
    14: 0.0740000000000000
    13: 0.0570000000000000
    12: 0.0440000000000000
    11: 0.0370000000000000
    9: 0.0220000000000000
    10: 0.0170000000000000
    8: 0.0030000000000000
    7: 0.0020000000000000
    mean = 15.999


  * Problem 3
    """
    ... This allows us to do inference even when the conditional is rare – for 
    instance if the team took out at least 55 orcs. 
    """

    Note: In Picat PPL, the min_accepted_samples is used to ensure a certain
          number of accepted samples. Here we ensure 1000 accepted samples

   var : gimli
   Probabilities:
   19: 0.6020000000000000
   18: 0.2850000000000000
   17: 0.1130000000000000
   mean = 18.489


*/
go ?=>
  member(Problem,1..3),
  println(problem=Problem),
  reset_store,
  Parameters = cond(Problem == 1,[show_probs,mean],
                                 [show_probs,mean,
                                  min_accepted_samples=1000 % ,show_accepted_samples=true
                                  ]),
  run_model(10_000,$model(Problem),Parameters),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
  
model(Problem) =>
  Legolas = discrete_uniform_dist(0,19),
  Gimli = discrete_uniform_dist(0,19),
  Eowyn = discrete_uniform_dist(0,19),
  TotalOrchs = Legolas + Gimli + Eowyn,

  if Problem == 2 then
    observe(TotalOrchs >= 45)
  end,
     
  if Problem == 3 then
    observe(TotalOrchs >= 55)
  end,
     
  if Problem == 1 ; observed_ok then
    add("gimli",Gimli),
    % add("total orchs",TotalOrchs),
  end.