/* 

  Firing squad example (Judea Pearl) in Picat.

  From Judea Pearl:
  court_order: a court order to shoot a prisoner is given
  captain_signals: captain signal to a and b to shoot the prisoner
  a_shoots: person a shoots at the prisoner
  b_shoots: person b shoots at the prisoner
  death: the prisoner is dead (due to the shooting of a and/or b)

  Cf my Gamble model gamble_firing_squad.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, ppl_common_utils.
import util.
% import ordset.

main => go.

/*
  [observation = 0,No observation]
  var : court order
  Probabilities:
  true: 0.7951000000000000
  false: 0.2049000000000000
  mean = 0.7951

  var : captain signals
  Probabilities:
  true: 0.7374000000000001
  false: 0.2626000000000000
  mean = 0.7374

  var : a shoots
  Probabilities:
  true: 0.7267000000000000
  false: 0.2733000000000000
  mean = 0.7267

  var : b shoots
  Probabilities:
  true: 0.7223000000000001
  false: 0.2777000000000000
  mean = 0.7223

  var : death
  Probabilities:
  true: 0.7012000000000000
  false: 0.2988000000000000
  mean = 0.7012


  [observation = 1,Death == true]
  var : court order
  Probabilities:
  true: 0.9361519782888159
  false: 0.0638480217111841
  mean = 0.936152

  var : captain signals
  Probabilities:
  true: 0.9414369375803456
  false: 0.0585630624196543
  mean = 0.941437

  var : a shoots
  Probabilities:
  true: 0.9267247536066276
  false: 0.0732752463933724
  mean = 0.926725

  var : b shoots
  Probabilities:
  true: 0.9271532638194544
  false: 0.0728467361805456
  mean = 0.927153

  var : death
  Probabilities:
  true: 1.0000000000000000
  mean = 1.0


  [observation = 2,Captain signals == false]
  var : court order
  Probabilities:
  false: 0.6979047619047619
  true: 0.3020952380952381
  mean = 0.302095

  var : captain signals
  Probabilities:
  false: 1.0000000000000000
  mean = 0.0

  var : a shoots
  Probabilities:
  false: 0.9165714285714286
  true: 0.0834285714285714
  mean = 0.0834286

  var : b shoots
  Probabilities:
  false: 0.9028571428571428
  true: 0.0971428571428571
  mean = 0.0971429

  var : death
  Probabilities:
  false: 0.8445714285714285
  true: 0.1554285714285714
  mean = 0.155429


  [observation = 3,BShoots == false]
  var : court order
  Probabilities:
  false: 0.6013488197826902
  true: 0.3986511802173098
  mean = 0.398651

  var : captain signals
  Probabilities:
  false: 0.8613713001124016
  true: 0.1386286998875984
  mean = 0.138629

  var : a shoots
  Probabilities:
  false: 0.7755713750468340
  true: 0.2244286249531660
  mean = 0.224429

  var : b shoots
  Probabilities:
  false: 1.0000000000000000
  mean = 0.0

  var : death
  Probabilities:
  false: 0.7954289996253279
  true: 0.2045710003746722
  mean = 0.204571


*/
go ?=>
  ObsMap = new_map([0="No observation",
                    1="Death == true",
                    2="Captain signals == false",
                    3="BShoots == false"]),
  member(Observation,0..3),
  println([observation=Observation,ObsMap.get(Observation)]),
  reset_store,
  run_model(10_000,$model(Observation),[show_probs_trunc,mean]),
  nl,
  fail,
  nl.
go => true.
  
  
model(Observation) =>
  CourtOrder = flip(0.8),
  CaptainSignals = cond(CourtOrder == true,flip(0.9),flip(0.1)),
  AShoots = cond(CaptainSignals == true,flip(0.95),flip(0.1)),
  BShoots = cond(CaptainSignals == true,flip(0.95),flip(0.1)),  

  % The prisoner don't die if neither A or B shoots
  Death = cond((AShoots == true ; BShoots == true),flip(0.9),false),


  if Observation == 1 then
    observe(Death == true)
  end,

  if Observation == 2 then
    observe(CaptainSignals == false)
  end,

  if Observation == 3 then
    observe(BShoots == false)
  end,

  if Observation == 0 ; observed_ok then
    add("court order",CourtOrder),
    add("captain signals",CaptainSignals),
    add("a shoots",AShoots),
    add("b shoots",BShoots),
    add("death",Death)
  end.