/* 

  Brian ate pizza last night in Picat.

  CUFP 2013: Avi Pfeffer: Functional Probabilistic Programming
  From https://www.youtube.com/watch?v=U67guma2H6s
  @3.56
  Brian ate pizza last night. Is he a programmer or a student?

  Cf my Gamble model gamble_brian_ate_pizza_last_night.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.
% import ordset.

main => go.

/*
  * obs = none
  var : student
  Probabilities:
  true: 0.6953000000000000
  false: 0.3047000000000000
  mean = [true = 0.6953,false = 0.3047]

  var : programmer
  Probabilities:
  false: 0.8277000000000000
  true: 0.1723000000000000
  mean = [false = 0.8277,true = 0.1723]

  var : student or programmer
  Probabilities:
  true: 0.7275000000000000
  false: 0.2725000000000000
  mean = [true = 0.7275,false = 0.2725]

  var : student and programmer
  Probabilities:
  false: 0.8599000000000000
  true: 0.1401000000000000
  mean = [false = 0.8599,true = 0.1401]

  var : pizza
  Probabilities:
  false: 0.6222000000000000
  true: 0.3778000000000000
  mean = [false = 0.6222,true = 0.3778]


  * obs = ate_pizza
  var : student
  Probabilities:
  true: 0.7630825305909920
  false: 0.2369174694090081
  mean = [true = 0.763083,false = 0.236917]

  var : programmer
  Probabilities:
  false: 0.6308253059099193
  true: 0.3691746940900807
  mean = [false = 0.630825,true = 0.369175]

  var : student or programmer
  Probabilities:
  true: 0.7870346263993752
  false: 0.2129653736006248
  mean = [true = 0.787035,false = 0.212965]

  var : student and programmer
  Probabilities:
  false: 0.6547774017183026
  true: 0.3452225982816975
  mean = [false = 0.654777,true = 0.345223]

  var : pizza
  Probabilities:
  true: 1.0000000000000000
  mean = [true = 1.0]

  So, since Brian ate pizza last night, he is probably a student and not a programmer: 
  the posterior is a little larger than the prior.


  * obs = not_ate_pizza
  var : student
  Probabilities:
  true: 0.6545454545454545
  false: 0.3454545454545455
  mean = [true = 0.654545,false = 0.345455]

  var : programmer
  Probabilities:
  false: 0.9390185036202735
  true: 0.0609814963797265
  mean = [false = 0.939019,true = 0.0609815]

  var : student or programmer
  Probabilities:
  true: 0.6897827835880933
  false: 0.3102172164119067
  mean = [true = 0.689783,false = 0.310217]

  var : student and programmer
  Probabilities:
  false: 0.9742558326629123
  true: 0.0257441673370877
  mean = [false = 0.974256,true = 0.0257442]

  var : pizza
  Probabilities:
  false: 1.0000000000000000
  mean = [false = 1.0]

  Then it's a little less likely that Brian is a student, and we are
  quite sure that he's not a programmer (p is about 0.06).


*/
go ?=>
  member(Obs,[none,ate_pizza,not_ate_pizza]),
  println(obs=Obs),
  reset_store,
  run_model(10_000,$model(Obs),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
  
model(Obs) =>
  Student    = flip(7/10),
  Programmer = cond(Student == true,flip(2/10),flip(1/10)),
  Pizza      = cond( (Student == true,Programmer == true), flip(9/10), flip(3/10)),

  if Obs == ate_pizza then
    % Brian ate pizza last night
    observe(Pizza == true)
  end,

  if Obs == not_ate_pizza then
    % Brian did not ate pizza last night    
    observe(Pizza == false)
  end,

  if Obs == none ; observed_ok then
    add("student",Student),
    add("programmer",Programmer),
    add("student or programmer",check( (Student ; Programmer))),
    add("student and programmer",check( (Student,Programmer))),
    add("pizza",Pizza)
  end.