/* 

  False coin in Picat.

  Inspired by Peter Winkler in
  From Celebration of Mind (Gathering For Gardner):
  "CoM Apr 2021 - Drawing from Urns - Peter Winkler"
  https://www.youtube.com/watch?v=A0GxvYPTKDk&list=PL5_D5QQxvWKVtX4Vklvhsf5KTYZBLDSwO&index=3

  Note: This is not what Peter talked about, but what I - wrongly - remembered. 
  See ppl_false_coin2.pi for this.

  *  We have one fake and one proper coin:
     1. head, head
     2. head, tail

  * We take one coin randomly and flip it: it's a head
  * To identify the fake coin, is it better to flip the same
    coin or flip the other coin?

  According to this model, it's better to throw the same coin again, i.e.
  coinB_switchIsFake: 1/3
  vs
  coinB_sameIsFake: 2/3


  Cf my Gamble model gamble_false_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.
import util.

main => go.

/*

  var : coinA
  Probabilities:
  1: 0.6615405188553090
  2: 0.3384594811446911
  mean = 1.33846
  variance = 0.223905

  var : sideA
  Probabilities:
  head: 1.0000000000000000
  mean = [head = 1.0]
  variance = data is not numeric

  var : coin B switch
  Probabilities:
  2: 0.6615405188553090
  1: 0.3384594811446911
  mean = 1.66154
  variance = 0.223905

  var : side B switch
  Probabilities:
  head: 0.6660871890879915
  tail: 0.3339128109120086
  mean = [head = 0.666087,tail = 0.333913]
  variance = data is not numeric

  var : coin B same
  Probabilities:
  1: 0.6615405188553090
  2: 0.3384594811446911
  mean = 1.33846
  variance = 0.223905

  var : side B same
  Probabilities:
  head: 0.8303022198448783
  tail: 0.1696977801551217
  mean = [head = 0.830302,tail = 0.169698]
  variance = data is not numeric

  var : coin B = switch coin
  Probabilities:
  0: 0.6615405188553090
  1: 0.3384594811446911
  mean = 0.338459
  variance = 0.223905

  var : coin B = same coin
  Probabilities:
  1: 0.6615405188553090
  0: 0.3384594811446911
  mean = 0.661541
  variance = 0.223905

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,variance]),
  nl,
  % show_store_lengths,
  % fail,
  nl.
go => true.
  

flip_coin(C) = cond(C,
                    categorical([1,0],[head,tail]),
                    categorical([1/2,1/2],[head,tail])).
model() =>
  % The two coins
  Coin1 = 1, % fake coin:   head,head
  Coin2 = 2, % proper coin: head,tail
  Coins = [Coin1,Coin2],

  % 1. Pick a coin randomly and flip it. It's head.
  CoinA = uniform_draw(Coins),
  SideA = flip_coin(CoinA == Coin1), % ???
  
  % We observe that the first flip was a head.
  observe(SideA == head),

  % 2a: Take the other coin and flip it.
  CoinBSwitch = cond(CoinA == Coin1, Coin2, Coin1),
  SideBSwitch = flip_coin(CoinBSwitch == Coin1),

  % 2b: Take the same coin and flip it.
  CoinBSame = CoinA,
  SideBSame = flip_coin(CoinBSame == Coin1),
  
  if observed_ok then
    add("coinA",CoinA),
    add("sideA",SideA),
    add("coin B switch",CoinBSwitch),
    add("side B switch",SideBSwitch),
    add("coin B same",CoinBSame),
    add("side B same",SideBSame),
    % Probability of fake coin
    add("coin B = switch coin",cond(CoinBSwitch == Coin1,1,0)),
    add("coin B = same coin",cond(CoinBSame == Coin1,1,0)),    
  end.