/* 

  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?


  Cf my Gamble model gamble_dice_6_throws.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.

/*

  [t_val = 0,v_val = 1,obs_list = [[0,1,true]]]
  var : on(tval,vval)
  Probabilities:
  false: 0.8395473496128648
  true: 0.1604526503871352
  mean = [false = 0.839547,true = 0.160453]


  [t_val = 1,v_val = 1,obs_list = [[0,1,true]]]
  var : on(tval,vval)
  Probabilities:
  false: 0.8572634625821625
  true: 0.1427365374178375
  mean = [false = 0.857263,true = 0.142737]


  [t_val = 2,v_val = 1,obs_list = [[0,1,true]]]
  var : on(tval,vval)
  Probabilities:
  false: 0.8861822763544729
  true: 0.1138177236455271
  mean = [false = 0.886182,true = 0.113818]


  [t_val = 2,v_val = 1,obs_list = [[0,1,true],[1,1,true],[2,1,true]]]
  var : on(tval,vval)
  Probabilities:
  false: 0.8842105263157894
  true: 0.1157894736842105
  mean = [false = 0.884211,true = 0.115789]


*/
go ?=>
  member([TVal,VVal,ObsList], [ [0,1,[[0,1,true]]],
                                [1,1,[[0,1,true]]],
                                [2,1,[[0,1,true]]],
                                [2,1,[[0,1,true],[1,1,true],[2,1,true]]]
                               ]
                               ),

  println([t_val=TVal,v_val=VVal,obs_list=ObsList]),
  reset_store,
  run_model(100_000,$model(TVal,VVal,ObsList),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
% Throw a singe die
throw_die(T) = categorical([1,1,1,1,1,1],1..6).

on(T,V) = Res =>
  ThrowDieT = throw_die(T),
  if T == 0 then
    if ThrowDieT == V, V != 6 then
      Res = true
    else 
      Res = false
    end
  else
    % It's not a 6, it's V, and no previous 6s
    if ThrowDieT != 6, ThrowDieT == V, sum([cond(throw_die(P) == 6,1,0) : P in 0..T-1]) == 0 then
       Res = true            
    else
       Res = false
    end
  end.

model(TVal,VVal,ObsList) =>

  foreach([T,V,TT] in ObsList) 
    observe(on(T,V) == TT)  
  end,
  
  if ObsList.len == 0 ; observed_ok then
    add("on(tval,vval)",check(on(TVal,VVal))),
  end.