/* 

  Chicken pecking in Picat.

  From (PSI model) 
  "HACSTFB - Probabilistic Programming Language ψ"
  https://www.youtube.com/watch?v=COS5YThEm1A
  About @10:04 ff

  10 chicken are arranged in a ring. With probability 1/2 a chicken picks the 
  chicken at left and probability 1/2 at right,
  What is the probability of unpecked chickens?

  From the PSI model, probabilities of number of unpecked chicken = 0,1,2,3,4,5,6,7,8,9,10;
  E[r1_,r2_,r3_,r4_,r5_,r6_,r7_,r8_,r9_,r10_,r11_] = (1/256,5/64,55/128,25/64,25/256,0,0,0,0,0,0)
  (0.00390625,0.078125,0.4296875,0.390625,0.09765625,0,0,0,0,0,0)

  This is a port of my WebPPL model chicken_pecking.wppl

  This matched the exact PSI model (as well as the WebPPL model)
  (2 : 55/128 (0.4296875))
  (3 : 25/64 (0.390625))
  (4 : 25/256 (0.09765625))
  (1 : 5/64 (0.078125))
  (0 : 1/256 (0.00390625))
  (mean: 2.5)


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

/*

  var : unpecked
  Probabilities:
  2: 0.42640000000000000 (533 / 1250)
  3: 0.39379999999999998 (1969 / 5000)
  4: 0.09650000000000000 (193 / 2000)
  1: 0.07990000000000000 (799 / 10000)
  0: 0.00340000000000000 (17 / 5000)
  mean = 2.5001

*/
go ?=>
  reset_store(),
  N = 10,
  run_model(10_000,$model(N),[show_probs_rat,mean]),
  fail,  
  nl.
go => true.

% This was inspired by the PSI model (via the Gamble model)
model(N) =>
  %  Initialize all chickens to be unpecked
  Pecked = [false : _ in 1..N],
  
  % Flag the chicken that was picked upon
  foreach(I in 1..N)
    V = mod_replace(I + condt(flip(),-1,1),N),
    Pecked[V] := true
  end,

  % Update the value of unpecked chickens
  Unpecked = [cond(Pecked[I] == false,1,0) : I in 1..N].sum,
  add("unpecked",Unpecked).