/* 

  Murder mystery in Picat.

  From
  Andy Gordon:
  "Reverend Bayes, meet Countess Lovelace: Probabilistic Programming for Machine Learning"
  https://channel9.msdn.com/Events/Lang-NEXT/Lang-NEXT-2012/Reverend-Bayes-meet-Countess-Lovelace-Probabilistic-Programming-for-Machine-Learning
  Around @14:00

  """
  Miss Scarlett dunnit 30%. Col Mustard dunnit 70%.
  Scarlett uses gun 3%, uses pipe 97%.
  Mustard uses gun 80%, uses pipe 20%.
  ...
  We found a gun at the Scene.
  What is the probability that Scarlett dunnit?
  """



  * 

  This is a port of my Gamble model gamble_murder_mystery.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.

main => go.

/* 
  * Original question: we found a gun, what is the probability that Scarlet did it?

    var : mustard
    Probabilities:
    true: 0.7021313766596785
    false: 0.2978686233403214
    mean = [true = 0.702131,false = 0.297869]

    var : scarlett
    Probabilities:
    false: 0.9814814814814815
    true: 0.0185185185185185
    mean = [false = 0.981481,true = 0.0185185]

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

    var : withPipe
    Probabilities:
    false: 0.7819706498951782
    true: 0.2180293501048218
    mean = [false = 0.781971,true = 0.218029]

  * If we had found a pipe instead:

    var : mustard
    Probabilities:
    true: 0.6982276119402985
    false: 0.3017723880597015
    mean = [true = 0.698228,false = 0.301772]

    var : scarlett
    Probabilities:
    true: 0.6721082089552238
    false: 0.3278917910447761
    mean = [true = 0.672108,false = 0.327892]

    var : withGun
    Probabilities:
    false: 0.7140858208955224
    true: 0.2859141791044776
    mean = [false = 0.714086,true = 0.285914]

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

*/
go ?=>
  reset_store(),
  run_model(10_000,model,[show_probs_trunc,mean]),
  nl,
  % fail,
  nl.
go => true.

model() =>
  Scarlett = flip(0.30),
  Mustard  = flip(0.70),

  WithGun  = condt(Scarlett, flip(0.03), flip(0.80)),
  WithPipe = condt(Scarlett, flip(0.97), flip(0.20)),

  observe(WithGun),
  % observe(WithPipe),

  if observed_ok then
    add_all([["scarlett",Scarlett],
             ["mustard",Mustard],
             ["withPipe",WithPipe],
             ["withGun",WithGun]
            ])
  end.