/* 

  Murder mystery in Picat.

  From https://mbmlbook.com/MurderMystery.html
  
  Infer.Net code: 
  https://github.com/dotnet/mbmlbook/blob/main/src/1.%20A%20Murder%20Mystery/Program.cs
  """
  ;; Input probabilities
  (define priors = new MurdererProbs ( Grey = 0.3, Auburn = 0.7 );
  
  (define conditionalsWeapon = new Variables.ConditionalVariablesWeapon
  (
  RevolverGivenGrey = 0.9,
  DaggerGivenGrey = 0.1,
  RevolverGivenAuburn = 0.2,
  DaggerGivenAuburn = 0.8,
  );
  
  (define conditionalsHair = new Variables.ConditionalVariablesHair
  (
  HairGivenGrey = 0.5,
  HairGivenAuburn = 0.05
  );
  """

  Cf my Gamble model gamble_murder_mystery_mbmlbook.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.

/*

  [weapon_cond = false,hair_cond = false]
  var : murderer
  Probabilities:
  auburn: 0.7056000000000000
  grey: 0.2944000000000000
  mean = [auburn = 0.7056,grey = 0.2944]

  var : murderer grey
  Probabilities:
  false: 0.7056000000000000
  true: 0.2944000000000000
  mean = [false = 0.7056,true = 0.2944]

  var : murderer auburn
  Probabilities:
  true: 0.7056000000000000
  false: 0.2944000000000000
  mean = [true = 0.7056,false = 0.2944]

  var : weapon
  Probabilities:
  dagger: 0.5955000000000000
  revolver: 0.4045000000000000
  mean = [dagger = 0.5955,revolver = 0.4045]

  var : hair
  Probabilities:
  false: 0.8157000000000000
  true: 0.1843000000000000
  mean = [false = 0.8157,true = 0.1843]


  [weapon_cond = false,hair_cond = true]
  var : murderer
  Probabilities:
  grey: 0.8169312169312170
  auburn: 0.1830687830687831
  mean = [grey = 0.816931,auburn = 0.183069]

  var : murderer grey
  Probabilities:
  true: 0.8169312169312170
  false: 0.1830687830687831
  mean = [true = 0.816931,false = 0.183069]

  var : murderer auburn
  Probabilities:
  false: 0.8169312169312170
  true: 0.1830687830687831
  mean = [false = 0.816931,true = 0.183069]

  var : weapon
  Probabilities:
  revolver: 0.7835978835978836
  dagger: 0.2164021164021164
  mean = [revolver = 0.783598,dagger = 0.216402]

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


  [weapon_cond = true,hair_cond = false]
  var : murderer
  Probabilities:
  grey: 0.6607662463627546
  auburn: 0.3392337536372454
  mean = [grey = 0.660766,auburn = 0.339234]

  var : murderer grey
  Probabilities:
  true: 0.6607662463627546
  false: 0.3392337536372454
  mean = [true = 0.660766,false = 0.339234]

  var : murderer auburn
  Probabilities:
  false: 0.6607662463627546
  true: 0.3392337536372454
  mean = [false = 0.660766,true = 0.339234]

  var : weapon
  Probabilities:
  revolver: 1.0000000000000000
  mean = [revolver = 1.0]

  var : hair
  Probabilities:
  false: 0.6602812803103782
  true: 0.3397187196896218
  mean = [false = 0.660281,true = 0.339719]


  [weapon_cond = true,hair_cond = true]
  var : murderer
  Probabilities:
  grey: 0.9457579972183588
  auburn: 0.0542420027816412
  mean = [grey = 0.945758,auburn = 0.054242]

  var : murderer grey
  Probabilities:
  true: 0.9457579972183588
  false: 0.0542420027816412
  mean = [true = 0.945758,false = 0.054242]

  var : murderer auburn
  Probabilities:
  false: 0.9457579972183588
  true: 0.0542420027816412
  mean = [false = 0.945758,true = 0.054242]

  var : weapon
  Probabilities:
  revolver: 1.0000000000000000
  mean = [revolver = 1.0]

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

*/
go ?=>
  member(WeaponCond,[false,true]),
  member(HairCond,[false,true]),
  println([weapon_cond=WeaponCond,hair_cond=HairCond]),
  
  reset_store,
  run_model(10_000,$model(WeaponCond,HairCond),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  fail,
  nl.
go => true.
  
  
model(WeaponCond, HairCond) =>

  % Priors for the murderer
  Murderer = categorical([0.3,0.7],[grey,auburn]),

  MurdererGrey = check(Murderer == grey),
  MurdererAuburn = check(Murderer == auburn),

  % The weapon was found
  Weapon = condt(MurdererGrey,
                 categorical([0.9,0.1],[revolver,dagger]),
                 categorical([0.2,0.8],[revolver,dagger])),

  % Some hair was found
  Hair = condt(MurdererGrey,flip(0.5),flip(0.05)),

  Observed = false,
  if WeaponCond then
    observe(Weapon == revolver),
    Observed := true
  end,

  if HairCond then
    observe(Hair),
    Observed := true    
  end,

  if (Observed, observed_ok) ;not(Observed)
     then
    add("murderer",Murderer),
    add("murderer grey",MurdererGrey),
    add("murderer auburn",MurdererAuburn),
    add("weapon",Weapon),
    add("hair",Hair),
  end.