/* 

  Fairness hiring model 2 in Picat.

  Port of SPPL model
  https://github.com/probcomp/sppl/blob/master/examples/fairness-hiring-model-2.ipynb

  The SPPL model gives the following exact probabilities:
  p(hire): 0.911360805292618
  p(hire|male):0.9777674365554804
  p(hire|female):0.8449541740297555
  p(hire|female)/p(hire|male): 0.8641668176293485


  Cf my Gamble model gamble_fairness_hiring_model2.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 : is male
  Probabilities:
  true: 0.5004999999999999
  false: 0.4995000000000000
  mean = [true = 0.5005,false = 0.4995]
  variance = data is not numeric

  var : hire
  Probabilities:
  1: 0.9170000000000000
  0: 0.0830000000000000
  mean = 0.917
  variance = 0.076111

  var : college rank
  Probabilities (truncated):
  63.522618485694046: 0.0001000000000000
  59.734512029092933: 0.0001000000000000
  59.474353768162132: 0.0001000000000000
  58.880107878401475: 0.0001000000000000
  .........
  -9.721152107001046: 0.0001000000000000
  -10.080650359811671: 0.0001000000000000
  -11.042384482359189: 0.0001000000000000
  -12.614881112804525: 0.0001000000000000
  mean = 25.1249
  variance = 101.161

  var : years exp
  Probabilities (truncated):
  32.954534979760766: 0.0001000000000000
  31.684166226678663: 0.0001000000000000
  31.157106325935093: 0.0001000000000000
  30.475944598795543: 0.0001000000000000
  .........
  -5.350581737689481: 0.0001000000000000
  -5.376313057425978: 0.0001000000000000
  -5.489058773480666: 0.0001000000000000
  -6.487258033403403: 0.0001000000000000
  mean = 12.5994
  variance = 30.9411

  var : hire, is male
  Probabilities:
  [1,true]: 0.4884000000000000
  [1,false]: 0.4286000000000000
  [0,false]: 0.0709000000000000
  [0,true]: 0.0121000000000000
  mean = [[1,true] = 0.4884,[1,false] = 0.4286,[0,false] = 0.0709,[0,true] = 0.0121]
  variance = data is not numeric

  var : hire given male
  Probabilities:
  0: 0.5116000000000001
  1: 0.4884000000000000
  mean = 0.4884
  variance = 0.249865

  var : hire given female
  Probabilities:
  0: 0.5714000000000000
  1: 0.4286000000000000
  mean = 0.4286
  variance = 0.244902

  [female = 0.4286,male = 0.4884,female/male = 0.877559]



*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,variance]),
  nl,
  Store = get_store(),
  HireMale = Store.get("hire given male").mean,
  HireFemale = Store.get("hire given female").mean,
  println([female=HireFemale,male=HireMale,"female/male"=(HireFemale/HireMale)]),

  % show_store_lengths,
  % fail,
  nl.
go => true.
  
  
model() =>
  % Population model
  IsMale = flip(0.5),
  CollegeRank = normal_dist(25,10),
  YearsExp = condt(IsMale,normal_dist(15,5),normal_dist(10,5)),

  % Hiring decision
  Hire = cond( (CollegeRank <= 5 ; YearsExp > 5),1,0),

  HireGivenMale = cond((Hire==1,IsMale==true),1,0),
  HireGivenFemale = cond((Hire==1,IsMale==false),1,0),

  add("is male",IsMale),
  add("hire",Hire),                
  add("college rank",CollegeRank),
  add("years exp",YearsExp),
  add("hire, is male",[Hire,IsMale]),
  add("hire given male",HireGivenMale),
  add("hire given female",HireGivenFemale).