/* 

  Appears tall in Picat.

  From HAL-ProbLog example examples/appears_tall.pl  
  (https://bitbucket.org/pedrozudo/hal_problog/src/master/examples/appears_tall.pl)
  """
  2/5::male;3/5::female.

  normal(180,8)~height:-male.
  normal(160,8)~height:-female.
  is_tall:-male, height~=Height, conS(180<Height).
  is_tall:-female, height~=Height, conS(170<Height).
  appears_tall:- is_tall.
  3/10::appears_tall:-male.

  query(is_tall).
  query(appears_tall).
  """

  We check with no observation and the obervation: is_tall = true


  Cf my Gamble model gamble_appears_tall.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.

/*
  observation = none
  var : appears tall
  Probabilities:
  false: 0.6636000000000000
  true: 0.3364000000000000
  mean = [false = 0.6636,true = 0.3364]

  var : gender
  Probabilities:
  female: 0.5965000000000000
  male: 0.4035000000000000
  mean = [female = 0.5965,male = 0.4035]

  var : height
  Probabilities (truncated):
  209.494219717115953: 0.0001000000000000
  207.755007561625206: 0.0001000000000000
  205.586799076977314: 0.0001000000000000
  204.438807897600412: 0.0001000000000000
  .........
  134.1968876780752: 0.0001000000000000
  133.64478324064828: 0.0001000000000000
  133.384865290567006: 0.0001000000000000
  131.810397755542311: 0.0001000000000000
  mean = 168.536

  var : is tall
  Probabilities:
  false: 0.7186000000000000
  true: 0.2814000000000000
  mean = [false = 0.7186,true = 0.2814]


  observation = is_tall
  var : appears tall
  Probabilities:
  true: 1.0000000000000000
  mean = [true = 1.0]

  var : gender
  Probabilities:
  male: 0.7216266173752310
  female: 0.2783733826247690
  mean = [male = 0.721627,female = 0.278373]

  var : height
  Probabilities (truncated):
  205.97063638903856: 0.0003696857670980
  205.666150354896018: 0.0003696857670980
  205.654977812449943: 0.0003696857670980
  204.562262582212497: 0.0003696857670980
  .........
  170.033421846958078: 0.0003696857670980
  170.021855794438949: 0.0003696857670980
  170.018651853569622: 0.0003696857670980
  170.000340926121169: 0.0003696857670980
  mean = 182.826

  var : is tall
  Probabilities:
  true: 1.0000000000000000
  mean = [true = 1.0]

*/
go ?=>
  member(Observation,[none,is_tall]),
  println(observation=Observation),
  reset_store,
  run_model(10_000,$model(Observation),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
  
model(Observation) =>
  GenderList = [male,female],
  Gender = categorical([2/5,3/5],GenderList),
  Height = cond(Gender == male, normal_dist(180,8), normal_dist(160.8,8)),

  IsTall = cond(Gender == male,check(Height >= 180), check(Height >= 170)),
  AppearsTall = cases([[IsTall, true],
                       [Gender==male, flip(3/10)],
                       [true,false]]),

  if Observation != none then
    observe(IsTall == true)
  end,

  if ( (Observation == none) ; (Observation != none, observed_ok)) then
    add("gender",Gender),
    add("height",Height),
    add("appears tall",AppearsTall),
    add("is tall",IsTall)
  end.