/* 

  Dice 6 throws in Picat.

  http://cplint.eu/example/inference/dice.swinb
  """
  A six-sided die is repeatedly thrown until the outcome is six. 
  on(T,F) means that on the Tth throw the face F came out.
  """

  What is the probability that the die lands on face 1 at time 0?

  This is an alternative version compared to ppl_dice_6_throws.pi
  using a simple while loop instead of recursion.
  (There is a Gamble model named ppl_dice_6_throws2.pi but this
  current model is not a very faithful port of that).

  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.

/*

  var : len
  Probabilities:
  1: 0.1705000000000000
  2: 0.1358000000000000
  3: 0.1123000000000000
  4: 0.0953000000000000
  5: 0.0783000000000000
  6: 0.0684000000000000
  7: 0.0587000000000000
  8: 0.0467000000000000
  9: 0.0373000000000000
  10: 0.0320000000000000
  11: 0.0306000000000000
  12: 0.0224000000000000
  13: 0.0200000000000000
  14: 0.0164000000000000
  15: 0.0123000000000000
  17: 0.0101000000000000
  16: 0.0091000000000000
  18: 0.0071000000000000
  19: 0.0054000000000000
  20: 0.0053000000000000
  21: 0.0041000000000000
  23: 0.0034000000000000
  22: 0.0028000000000000
  24: 0.0026000000000000
  26: 0.0024000000000000
  25: 0.0019000000000000
  27: 0.0016000000000000
  28: 0.0009000000000000
  34: 0.0008000000000000
  30: 0.0008000000000000
  29: 0.0007000000000000
  31: 0.0006000000000000
  32: 0.0005000000000000
  35: 0.0004000000000000
  40: 0.0003000000000000
  38: 0.0003000000000000
  50: 0.0002000000000000
  46: 0.0002000000000000
  43: 0.0002000000000000
  37: 0.0002000000000000
  36: 0.0002000000000000
  33: 0.0002000000000000
  69: 0.0001000000000000
  56: 0.0001000000000000
  55: 0.0001000000000000
  45: 0.0001000000000000
  44: 0.0001000000000000
  42: 0.0001000000000000
  39: 0.0001000000000000
  mean = 6.0296

  var : p = 1
  Probabilities:
  true: 1.0000000000000000
  mean = [true = 1.0]

  var : throw 1 = 1
  Probabilities:
  false: 0.8386000000000000
  true: 0.1614000000000000
  mean = [false = 0.8386,true = 0.1614]

  var : throw 2 = 1
  Probabilities:
  false: 0.8622000000000000
  true: 0.1378000000000000
  mean = [false = 0.8622,true = 0.1378]

  var : throw 3 = 1
  Probabilities:
  false: 0.8790000000000000
  true: 0.1210000000000000
  mean = [false = 0.879,true = 0.121]

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

  Until6 = false,
  Throws = [],
  while (Until6 == false)
    D = dice(),
    Throws := Throws ++ [D],
    if D == 6 then
      Until6 := true
    end,
  end,

  Len = Throws.len,
  P = check(Throws.last == 6),
  On_1_1 = check(Throws[1] == 1),
  % Note: we can not use cond/3 here since Picat
  %       then complain if then length is 1.
  if Len >= 2 then
    On_2_1 = check(Throws[2] == 1)
  else
    On_2_1 = false
  end,
  if Len >= 3 then
    On_3_1 = check(Throws[3] == 1)
  else
    On_3_1 = false
  end,

  add("len",Len),
  add("p = 1",P),  
  add("throw 1 = 1",On_1_1),
  add("throw 2 = 1",On_2_1),
  add("throw 3 = 1",On_3_1).