/* 

  Simple Caesar cipher in Picat.

  Port of Dice model
  https://github.com/SHoltzen/dice/blob/master/benchmarks/simpleCaesar.dice

  Cf my Gamble model gamble_caesar.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.
% import ordset.

main => go.

/*


*/
go ?=>
  reset_store,
  run_model(100_000,$model,[show_probs_trunc,mean,
                           % show_percentiles,show_histogram,
                           % show_hpd_intervals,hpd_intervals=[0.84],
                           min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.


draw_char(Key,Observation) = Res =>
  S = [0.08167,0.01492,0.02782,0.04253,0.04378,0.02228,0.02015,0.06094,
       0.06966,0.0153,0.0772,0.04025,0.02406,0.06749,0.07507,0.01929,
       0.00095,0.05987,0.06327,0.09056,0.02758,0.00978,0.02360,0.00150,
       0.01974,0.00074],
  Len = S.len,
  DrawnChar = categorical(S,0..Len-1),
  Encrypted = Key + DrawnChar,
  observe(Encrypted == Observation),
  Res = Encrypted.
  
model() =>
  Len = 26,
  Key1 = categorical(ones(Len,1),0..Len-1),
  % We only do one observation here

  Observation = draw_char(Key1,2),

  if observed_ok then
    add("key1",Key1),
    add("observation",Observation),    
  end.

/*
  Here is a simpler version from http://dicelang.cs.ucla.edu/
  

  reps = 1
  var : key
  Probabilities:
  3: 0.5068163592622293
  2: 0.2481956696070569
  0: 0.1279069767441861
  1: 0.1170809943865277
  mean = 2.13392


  reps = 2
  var : key
  Probabilities:
  3: 0.7539682539682540
  2: 0.1746031746031746
  0: 0.0374149659863946
  1: 0.0340136054421769
  mean = 2.64512


  reps = 3
  var : key
  Probabilities:
  3: 0.8739255014326648
  2: 0.0945558739255014
  0: 0.0171919770773639
  1: 0.0143266475644699
  mean = 2.82521


  reps = 4
  var : key
  Probabilities:
  3: 0.9806451612903225
  2: 0.0193548387096774
  mean = 2.98065

*/
go2 ?=>
  member(Reps,1..4),
  println(reps=Reps),
  reset_store,
  run_model(10_000,$model2(Reps),[show_probs_trunc,mean % ,
                           % show_percentiles,show_histogram,
                           % show_hpd_intervals,hpd_intervals=[0.84],
                            %min_accepted_samples=1000,show_accepted_samples=false
                          ]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go2 => true.

send_char(Key,Observation) = Res =>
  Gen = categorical([0.5,0.25,0.125,0.125],0..3),
  Enc = Key + Gen,
  observe(Observation == Enc),
  Res = Enc.

model2(Reps) =>
  N = 4,
  Key = categorical(ones(N,1),0..N-1),
  Os = [],
  foreach(I in 1..Reps)
   O = send_char(Key,3),
   Os := Os ++ [O]
  end,

  if observed_ok then
    add("key",Key),
  end.