/* 

  Biased coin in Picat.

  From cplint: http://cplint.eu/example/inference/coin.pl
  """
  Throwing a coin with uncertainty on its fairness, from
  J. Vennekens, S. Verbaeten, and M. Bruynooghe. Logic programs with annotated
  disjunctions. In International Conference on Logic Programming,
  volume 3131 of LNCS, pages 195-209. Springer, 2004.
  """

  From the cplint model:
  """
  heads(Coin): 1/2; tails(Coin) : 1/2:-toss(Coin),\+biased(Coin).
  % if we toss a Coin that is not biased then it lands heads with probability 1/2
  % and tails with probability 1/2

  heads(Coin): 0.6 ; tails(Coin) : 0.4:-toss(Coin),biased(Coin).
  % if we toss a Coin that is biased then it lands heads with probability 0.6
  % % and tails with probability 0.4
  
  fair(Coin):0.9 ; biased(Coin):0.1.
  % a Coin is fair with probability 0.9 and biased with probability 0.1
  
  toss(coin).
  % coin is certainly tossed
  

  ?- prob(heads(coin),Prob).  % what is the probability that coin lands heads?
  % expected result 0.51
  
  ?- prob(tails(coin),Prob).  % what is the probability that coin lands tails?
  % expected result 0.49
  
  calculation: is fair and tail 0.9*0.5 + biased and tail 0.1*0.4 = 0.9*0.5 +  0.1*0.4 = 0.49
  
  ?- prob(heads(coin),biased(coin),Prob).
  % what is the probability that coin lands heads given the coin is biased?
  % expected result 0.6
  """

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

/*

no observation
Var coin_result:
Probabilities:
head: 0.5087000000000000
tail: 0.4913000000000000
mean = not_numeric
Histogram:
head      :  5087 ############################################################ (0.509 / 0.509)
tail      :  4913 ##########################################################   (0.491 / 1.000)

Var coin_type:
Probabilities:
fair: 0.8981000000000000
biased: 0.1019000000000000
mean = not_numeric
Histogram:
biased    :  1019 #######                                                      (0.102 / 0.102)
fair      :  8981 ############################################################ (0.898 / 1.000)


observe biased
Var coin_result:
Probabilities:
head: 0.6115459882583171
tail: 0.3884540117416830
mean = not_numeric
Histogram:
head      :   625 ############################################################ (0.612 / 0.612)
tail      :   397 ######################################                       (0.388 / 1.000)

Var coin_type:
Probabilities:
biased: 1.0000000000000000
mean = not_numeric
Histogram:
biased    :  1022 ############################################################ (1.000 / 1.000)

*/
go ?=>
  member(Experiment,["no observation","observe biased"]),
  println(Experiment),
  reset_store,
  run_model(10_000,$biased_coin(Experiment),[show_probs,mean,show_histogram]),
  fail,  
  nl.
go => true.
  
  
biased_coin(Experiment) =>
  CoinType = categorical([9/10,1/10],["fair","biased"]),
  CoinResult = cond(CoinType == "fair",
                    categorical([1/2,1/2],["head","tail"]),
                    categorical([6/10,4/10],["head","tail"])),
  if Experiment == "observe biased" then
    if CoinType == "biased" then
      add("coin_type",CoinType),
      add("coin_result",CoinResult)
    end
  else
    add("coin_type",CoinType),
    add("coin_result",CoinResult)
  end.