/* 

  Bugs book example 2.4.1 Transformation in Picat.

  Cf my Gamble model gamble_bugs_book_2_4_1.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.

/*

  var : p10
  Probabilities:
  false: 0.7231000000000000
  true: 0.2769000000000000
  mean = [false = 0.7231,true = 0.2769]
  HPD intervals:
  show_hpd_intervals: data is not numeric

  var : y
  Probabilities (truncated):
  509.531914367826516: 0.0001000000000000
  412.444264558721386: 0.0001000000000000
  409.362911610060223: 0.0001000000000000
  372.156640358727657: 0.0001000000000000
  .........
  -204.419069361638179: 0.0001000000000000
  -220.770224992962142: 0.0001000000000000
  -234.403807044124875: 0.0001000000000000
  -271.912507637484111: 0.0001000000000000
  mean = 12.4619
  HPD intervals:
  HPD interval (0.84): -11.70512322128070..39.18030029671765

  var : z
  Probabilities (truncated):
  3.493562338352659: 0.0001000000000000
  3.221846240016826: 0.0001000000000000
  3.212554478857002: 0.0001000000000000
  3.096487830930652: 0.0001000000000000
  .........
  -3.445396772531768: 0.0001000000000000
  -3.521923767488838: 0.0001000000000000
  -3.582891388681194: 0.0001000000000000
  -3.7392644095049: 0.0001000000000000
  mean = -0.00352527
  HPD intervals:
  HPD interval (0.84): -1.44174426750184..1.32977645195029

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,show_hpd_intervals,hpd_intervals=[0.84]]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Z = normal_dist(0,1),
  Y = ((2 * Z) + 1) ** 3,
  P10 = check(Y > 10),
  
  add("p10",P10),
  add("y",Y),
  add("z",Z).