/* 

  Who killed the Bosmer problem in Picat.

  From https://swi-prolog.discourse.group/t/similar-einstein-riddle/5142/6
  """
  A Bosmer, was slain. The Altmer claims the Dunmer is guilty. The Dunmer says 
  the Khajiit did it. The Orc swears he didn’t kill the Bosmer. The Khajiit says 
  the Dunmer is lying. If only one of these speaks the truth, who killed 
  the Bosmer?
  """

  Port of my Gamble model gamble_who_killed_the_bosmer.rkt.

  Compare with my Picat CP model  who_killed_the_bosmer.pi

  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.

main => go.

/*
  I.e. Orc is Guilty, and Khajiit speaks the truth.

var : AltmerG
Probabilities:
0: 1.00000000000000000 (1 / 1)

var : AltmerT
Probabilities:
0: 1.00000000000000000 (1 / 1)

var : DunmerG
Probabilities:
0: 1.00000000000000000 (1 / 1)

var : DunmerT
Probabilities:
0: 1.00000000000000000 (1 / 1)

var : Guilty
Probabilities:
Orc: 1.00000000000000000 (1 / 1)

var : KhajiitG
Probabilities:
0: 1.00000000000000000 (1 / 1)

var : KhajiitT
Probabilities:
1: 1.00000000000000000 (1 / 1)

var : OrcG
Probabilities:
1: 1.00000000000000000 (1 / 1)

var : OrcT
Probabilities:
0: 1.00000000000000000 (1 / 1)

var : SpeaksTruth
Probabilities:
Khajiit: 1.00000000000000000 (1 / 1)



*/
go ?=>
  reset_store(),
  run_model(20_000,$model,[show_probs_rat]),
  fail,
  nl.
go => true.



model() =>
  P = 1/2, % Prior probability
  People = ["Altmer","Dunmer","Orc","Khajiit"],  
  
  %  Speaks the truth?
  AltmerT  = bernoulli_dist(P),
  DunmerT  = bernoulli_dist(P),
  OrcT     = bernoulli_dist(P),
  KhajiitT = bernoulli_dist(P),
   
  % Is guilty?
  AltmerG  = bernoulli_dist(P),
  DunmerG  = bernoulli_dist(P),
  OrcG     = bernoulli_dist(P),
  KhajiitG = bernoulli_dist(P),

  % A Bosmer, was slain.
  
  if 
    % The Altmer claims the Dunmer is guilty.
    AltmerT == DunmerG,
   
    % The Dunmer says the Khajiit did it.
    DunmerT == KhajiitG,
   
    % The Orc swears he didn’t kill the Bosmer.
    cond(OrcG == 0,true,false) == cond(OrcT == 1,true,false),
   
    %  The Khajiit says the Dunmer is lying.
    cond(DunmerT == 0,true,false) == cond(KhajiitT == 1,true,false),
   
    %  If only one of these speaks the truth, who killed the Bosmer?""
    AltmerT + DunmerT + OrcT + KhajiitT == 1,
    AltmerG + DunmerG + OrcG + KhajiitG == 1 then

    SpeaksTruth = [ Person : {Person,T} in zip(People,[AltmerT,DunmerT,OrcT, KhajiitT]), T == 1].first,
    Guilty = [ Person : {Person,G} in zip(People,[AltmerG,DunmerG,OrcG, KhajiitG]), G == 1].first,
  add_all([ ["AltmerT",AltmerT],
            ["DunmerT",DunmerT],
            ["OrcT",OrcT],
            ["KhajiitT",KhajiitT],
            ["AltmerG",AltmerG],
            ["DunmerG",DunmerG],
            ["OrcG",OrcG],
            ["KhajiitG",KhajiitG],
            ["SpeaksTruth",SpeaksTruth],
            ["Guilty",Guilty]])
  end.