/* 

  Person login in Picat.

  From Yi Wu, Lei Li, Stuart Russell
  "BFiT: From Possible-World Semantics to Random-Evaluation Semantics in Open Universe"
  Page 3

  Cf my Gamble model gamble_person_login.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 : num_people
Probabilities (truncated):
5: 0.1803000000000000
6: 0.1774000000000000
7: 0.1442000000000000
4: 0.1436000000000000
.........
13: 0.0033000000000000
14: 0.0020000000000000
15: 0.0004000000000000
17: 0.0001000000000000
mean = 5.9559
Histogram:
      1:    72 ##                                                           (0.007 / 0.007)
      2:   353 ############                                                 (0.035 / 0.042)
      3:   828 ############################                                 (0.083 / 0.125)
      4:  1436 ################################################             (0.144 / 0.269)
      5:  1803 ############################################################ (0.180 / 0.449)
      6:  1774 ###########################################################  (0.177 / 0.627)
      7:  1442 ################################################             (0.144 / 0.771)
      8:  1002 #################################                            (0.100 / 0.871)
      9:   638 #####################                                        (0.064 / 0.935)
     10:   350 ############                                                 (0.035 / 0.970)
     11:   172 ######                                                       (0.017 / 0.987)
     12:    72 ##                                                           (0.007 / 0.994)
     13:    33 #                                                            (0.003 / 0.997)
     14:    20 #                                                            (0.002 / 0.999)
     15:     4                                                              (0.000 / 1.000)
     17:     1                                                              (0.000 / 1.000)

var : sample_login
Probabilities:
1: 0.9179000000000000
0: 0.0784000000000000
2: 0.0030000000000000
4: 0.0004000000000000
3: 0.0003000000000000
mean = 0.9264
Histogram:
      0:   784 #####                                                        (0.078 / 0.078)
      1:  9179 ############################################################ (0.918 / 0.996)
      2:    30                                                              (0.003 / 0.999)
      3:     3                                                              (0.000 / 1.000)
      4:     4                                                              (0.000 / 1.000)

var : num_honest
Probabilities (truncated):
5: 0.1868000000000000
4: 0.1759000000000000
6: 0.1638000000000000
7: 0.1262000000000000
.........
13: 0.0022000000000000
0: 0.0011000000000000
14: 0.0007000000000000
15: 0.0002000000000000
mean = 5.3631
Histogram:
      0:    11                                                              (0.001 / 0.001)
      1:   160 #####                                                        (0.016 / 0.017)
      2:   594 ###################                                          (0.059 / 0.076)
      3:  1160 #####################################                        (0.116 / 0.193)
      4:  1759 ########################################################     (0.176 / 0.368)
      5:  1868 ############################################################ (0.187 / 0.555)
      6:  1638 #####################################################        (0.164 / 0.719)
      7:  1262 #########################################                    (0.126 / 0.845)
      8:   765 #########################                                    (0.076 / 0.922)
      9:   440 ##############                                               (0.044 / 0.966)
     10:   194 ######                                                       (0.019 / 0.985)
     11:    85 ###                                                          (0.009 / 0.994)
     12:    33 #                                                            (0.003 / 0.997)
     13:    22 #                                                            (0.002 / 0.999)
     14:     7                                                              (0.001 / 1.000)
     15:     2                                                              (0.000 / 1.000)

var : honest_sample_login
Probabilities:
true: 0.9179000000000000
false: 0.0821000000000000
mean = [true = 0.9179,false = 0.0821]
Histogram:
false     :   821 #####                                                        (0.082 / 0.082)
true      :  9179 ############################################################ (0.918 / 1.000)

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,show_histogram]),
  nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  % Number of people
  NumPeople = poisson_dist(5)+1,

  % Is this person honest?
  Honest = [ flip(0.9) : _ in 1..NumPeople],

  % How many are honest?
  NumHonest = [condt(Honest[P],1,0) : P in 1..NumPeople].sum,
  
  % An honest person have just one login
  Login = [ condt(Honest[P],1, geometric_dist(0.8)) : P in 1..NumPeople],
  
  % Pick one person
  SampleLogin = uniform_draw(Login),
  HonestSampleLogin = check(SampleLogin==1),

  add("num_people",NumPeople),
  add("sample_login",SampleLogin),
  add("num_honest",NumHonest),
  add("honest_sample_login",HonestSampleLogin).