/* 

  Probabilistic graphs in Picat.

  https://dtai.cs.kuleuven.be/problog/tutorial/basic/04_pgraph.html
  ProbLog model:
  """
  0.6::edge(1,2).
  0.1::edge(1,3).
  0.4::edge(2,5).
  0.3::edge(2,6).
  0.3::edge(3,4).
  0.8::edge(4,5).
  0.2::edge(5,6).

  path(X,Y) :- edge(X,Y).
  path(X,Y) :- edge(X,Z),
               Y \== Z,
               path(Z,Y).

  query(path(1,5)).
  query(path(1,6)).
  query(path(5,2)).
  """
 
  Results from the ProbLog model
  """
  path(1,5): 0.25824    (i.e. 0->4)
  path(1,6): 0.2167296  (i.e. 0->5)
  """

  Cf my Gamble model gamble_probabilistic_graphs.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.

/*
  Paths: 1->6 and 1->6

  var : path 1-> 5
  Probabilities:
  false: 0.7421000000000000
  true: 0.2579000000000000
  mean = [false = 0.7421,true = 0.2579]

  var : path 1-> 6
  Probabilities:
  false: 0.7841000000000000
  true: 0.2159000000000000
  mean = [false = 0.7841,true = 0.2159]

  All paths:

path 1 -> 1
var : p
Probabilities:
false: 1.0000000000000000


path 1 -> 2
var : p
Probabilities:
true: 0.5998000000000000
false: 0.4002000000000000


path 1 -> 3
var : p
Probabilities:
false: 0.8961000000000000
true: 0.1039000000000000


path 1 -> 4
var : p
Probabilities:
false: 0.9706000000000000
true: 0.0294000000000000


path 1 -> 5
var : p
Probabilities:
false: 0.7441000000000000
true: 0.2559000000000000


path 1 -> 6
var : p
Probabilities:
false: 0.7853000000000000
true: 0.2147000000000000


path 2 -> 1
var : p
Probabilities:
false: 1.0000000000000000


path 2 -> 2
var : p
Probabilities:
false: 1.0000000000000000


path 2 -> 3
var : p
Probabilities:
false: 1.0000000000000000


path 2 -> 4
var : p
Probabilities:
false: 1.0000000000000000


path 2 -> 5
var : p
Probabilities:
false: 0.5936000000000000
true: 0.4064000000000000


path 2 -> 6
var : p
Probabilities:
false: 0.6460000000000000
true: 0.3540000000000000


path 3 -> 1
var : p
Probabilities:
false: 1.0000000000000000


path 3 -> 2
var : p
Probabilities:
false: 1.0000000000000000


path 3 -> 3
var : p
Probabilities:
false: 1.0000000000000000


path 3 -> 4
var : p
Probabilities:
false: 0.7027000000000000
true: 0.2973000000000000


path 3 -> 5
var : p
Probabilities:
false: 0.7625000000000000
true: 0.2375000000000000


path 3 -> 6
var : p
Probabilities:
false: 0.9558000000000000
true: 0.0442000000000000


path 4 -> 1
var : p
Probabilities:
false: 1.0000000000000000


path 4 -> 2
var : p
Probabilities:
false: 1.0000000000000000


path 4 -> 3
var : p
Probabilities:
false: 1.0000000000000000


path 4 -> 4
var : p
Probabilities:
false: 1.0000000000000000


path 4 -> 5
var : p
Probabilities:
true: 0.8014000000000000
false: 0.1986000000000000


path 4 -> 6
var : p
Probabilities:
false: 0.8398000000000000
true: 0.1602000000000000


path 5 -> 1
var : p
Probabilities:
false: 1.0000000000000000


path 5 -> 2
var : p
Probabilities:
false: 1.0000000000000000


path 5 -> 3
var : p
Probabilities:
false: 1.0000000000000000


path 5 -> 4
var : p
Probabilities:
false: 1.0000000000000000


path 5 -> 5
var : p
Probabilities:
false: 1.0000000000000000


path 5 -> 6
var : p
Probabilities:
false: 0.7960000000000000
true: 0.2040000000000000


path 6 -> 1
var : p
Probabilities:
false: 1.0000000000000000


path 6 -> 2
var : p
Probabilities:
false: 1.0000000000000000


path 6 -> 3
var : p
Probabilities:
false: 1.0000000000000000


path 6 -> 4
var : p
Probabilities:
false: 1.0000000000000000


path 6 -> 5
var : p
Probabilities:
false: 1.0000000000000000


path 6 -> 6
var : p
Probabilities:
false: 1.0000000000000000


*/
go ?=>
  N = 6,
  member(I,1..N),
  member(J,1..N),
  printf("path %d -> %d\n",I,J),
  reset_store,
  run_model(10_000,$model(I,J),[show_probs_trunc]),
  nl,
  % show_store_lengths,
  fail,
  nl.
go => true.
  

edge(T1,T2,M) = flip(M[T1,T2]).

path(T1,T2,M,Edges) = Ret =>
  if edge(T1,T2,M) == true then
    Ret = true
  else
    if member(T3,Edges), T2 != T3, T1 != T3,
       edge(T1,T3,M) == true,path(T3,T2,M,Edges) == true
       then
      Ret = true
    else
      Ret = false
    end
  end.
model(I,J) =>
  

   % Graph
   %  1 -> 2,3
   %  2 -> 5,6
   %  3 -> 4
   %  4 -> 5
   %  5 -> 6
   %  6 -> ()   
   M = [
         %% 1    2    3    4    5    6 
         [0.0, 0.6, 0.1, 0.0, 0.0, 0.0], % 1
         [0.0, 0.0, 0.0, 0.0, 0.4, 0.3], % 2
         [0.0, 0.0, 0.0, 0.3, 0.0, 0.0], % 3
         [0.0, 0.0, 0.0, 0.0, 0.8, 0.0], % 4
         [0.0, 0.0, 0.0, 0.0, 0.0, 0.2], % 5
         [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]  % 6
       ],
   N = M.len,
   Edges = 1..N,
  % P1_5 = path(1,5,M,Edges),
  % P1_6 = path(1,6,M,Edges),
  % add("path 1-> 5",P1_5),
  % add("path 1-> 6",P1_6).
  add("p",path(I,J,M,Edges)).
  % foreach(I in 1..N, J in 1..N)
  %  add("path "++ I.to_string ++ "-> " ++ J.to_string,path(I,J,M,Edges)),
  % end.