/* 

  Rolling dice problem in Picat.

  https://dtai.cs.kuleuven.be/problog/tutorial/basic/03_dice.html
  """
  The following example illustrates the use of a logic program with recursion and lists. 
  We start by rolling the first die. Every roll determines the next die to roll, but we stop 
  if we have used that die before. We query for the possible sequences of rolled dice. 
  We use three-sided dice instead of the regular six-sided ones simply to restrict the number 
  of possible outcomes (and thus inference time). 
  """


  Cf my Gamble model gamble_rolling_dice_problem.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.

main => go.

/*
  Here we test some different sizes (2, 5, 8, 11) without and with
  the observation that the first element in the array is 1.
  Though there don't seems to be any difference between the
  two cases (of not observed and observed).
 
  [n = 2,observation = false]
  var : len
  Probabilities:
  3: 0.5051000000000000
  2: 0.4949000000000000
  mean = 2.5051


  [n = 2,observation = true]
  var : len
  Probabilities:
  3: 0.5020820939916716
  2: 0.4979179060083284
  mean = 2.50208


  [n = 5,observation = false]
  var : len
  Probabilities:
  3: 0.3191000000000000
  4: 0.2942000000000000
  2: 0.1940000000000000
  5: 0.1531000000000000
  6: 0.0396000000000000
  mean = 3.5252


  [n = 5,observation = true]
  var : len
  Probabilities:
  3: 0.3297764227642276
  4: 0.2840447154471545
  2: 0.1854674796747967
  5: 0.1620934959349593
  6: 0.0386178861788618
  mean = 3.53862


  [n = 8,observation = false]
  var : len
  Probabilities:
  4: 0.2491000000000000
  3: 0.2160000000000000
  5: 0.2065000000000000
  6: 0.1290000000000000
  2: 0.1223000000000000
  7: 0.0575000000000000
  8: 0.0173000000000000
  9: 0.0023000000000000
  mean = 4.2571


  [n = 8,observation = true]
  var : len
  Probabilities:
  4: 0.2410646387832700
  3: 0.2197718631178707
  5: 0.2098859315589354
  2: 0.1209125475285171
  6: 0.1193916349809886
  7: 0.0646387832699620
  8: 0.0220532319391635
  9: 0.0022813688212928
  mean = 4.28061


  [n = 11,observation = false]
  var : len
  Probabilities:
  4: 0.2005000000000000
  5: 0.1975000000000000
  3: 0.1652000000000000
  6: 0.1531000000000000
  7: 0.0983000000000000
  2: 0.0976000000000000
  8: 0.0515000000000000
  9: 0.0269000000000000
  10: 0.0074000000000000
  11: 0.0020000000000000
  mean = 4.8371


  [n = 11,observation = true]
  var : len
  Probabilities:
  5: 0.2014051522248244
  4: 0.1873536299765808
  3: 0.1697892271662763
  6: 0.1451990632318501
  7: 0.1018735362997658
  2: 0.0936768149882904
  8: 0.0620608899297424
  9: 0.0327868852459016
  11: 0.0035128805620609
  10: 0.0023419203747073
  mean = 4.8911



*/
go ?=>
  member(N,2..3..11),
  member(Obs,[false,true]),
  println([n=N,observation=Obs]),
  reset_store,
  run_model(10_000,$model(N,Obs),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  fail,
  nl.
go => true.
  

roll(A,N) = Ret =>
  if A.len != A.remove_dups.len then
    Ret = A
  else
    Ret = roll(A++[random_integer1(N)],N)
  end.
model(N,Obs) =>
  A = roll([],N),

  if Obs == true then
    observe(A[1] == 1),
    if observed_ok then
      add("len",A.len)
    end
  else
    add("len",A.len)
  end.