/* 

  Number guessing game in Picat.

  https://social.microsoft.com/Forums/en-US/a76a904d-ae2e-4118-bec0-c928772d7ff7/solving-the-nested-number-guessing-problem-from-anglican-web-site?forum=infer.net
  """
  I'm trying to express with Infer.NET one of the examples in the Anglican web site:
     http://www.robots.ox.ac.uk/~fwood/anglican/examples/viewer/?worksheet=nested-number-guessing

  Here the description of the problems:
    "Two agents play a game in which each agent needs to name a number between 0 and 9 and they win
     if their numbers add up to 13. The first player knows this, and he knows that the second player
     gets to see the number the first player chooses, but the second player mistakenly thinks that
     the two win if their numbers add up to any number greater than 8 (and the first player knows
     this as well). What number should the first player choose?
  """ 


  Cf the Church model http://forestdb.org/models/nested-guessing.html
  """
  (define (sample)
  (rejection-query
   (define a (sample-integer 10))
   (define b
     (rejection-query
      (define c (sample-integer 10))
      c
      (> (+ a c) 8)))
   a
   (= (+ a b) 13)))

  (hist (repeat 10000 sample))
  """

  References:
  Reasoning about Reasoning by Nested Conditioning: Modeling Theory of Mind with Probabilistic 
  Programs. Andreas Stuhlmüller and Noah D. Goodman (2013). Cognitive Systems Research.
  [http://www.mit.edu/~ast/papers/nested-conditioning-cogsys2013.pdf]

  Cf 
  - my Gamble model gamble_number_guessing_game.rkt
  - my WebPPL model number_guessing_game.wppl
  - my PSI model number_guessing_game.psi

  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.

/*
  This is a port of the Church mode and my Gamble model. 

  var : a
  Probabilities:
  4: 0.1923000000000000
  5: 0.1862000000000000
  6: 0.1761000000000000
  7: 0.1652000000000000
  8: 0.1443000000000000
  9: 0.1359000000000000
  mean = 6.2907

  I.e. the player should pick the number 4.

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

%
% In the Church and Gamble models, this
% was a model using rejection sampling.
% In Picat PPL, we have to do this
% in a different way...
%
b(A) = Res =>
  C = random_integer(10),
  % Ensure A + C > 8
  if not (A + C > 8) then
    C := random_integer(10),
  end,
  Res = C.

model() =>
  A = random_integer(10),
  B = b(A),
  
  observe(A + B == 13),

  if observed_ok then
    add("a",A),
  end.


/*
  A variant (from my WebPPL model number_guessing_game.wppl)

  var : b
  Probabilities:
  4: 0.2183000000000000
  5: 0.1992000000000000
  6: 0.1837000000000000
  7: 0.1511000000000000
  8: 0.1312000000000000
  9: 0.1165000000000000
  mean = 6.1272



*/
go2 ?=>
  reset_store,
  run_model(10_000,$model2,[show_probs_trunc,mean,
                           min_accepted_samples=10_000 % ,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go2 => true.


model2() =>
  A = random_integer(10),
  B = random_integer(10),
  C = random_integer(10),  

  observe(A + C > 8),   % player a thinks that they win if a+b > 8 (this is a mistake)
  observe(A + B == 13), % player b knows that it's the sum of 13 that's the goal

  if observed_ok then
    add("b",B),
  end.