/* 

  Number of fix points in Picat.

  A fix point is - here - when the I'th element is assigned to I, i.e.
    X[I] #= I

  It can, for example, be used together with subcircuit to constraint the
  of solutions.

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.


main => go.

go ?=>
  N = 7,

  X = new_list(N),
  X :: 1..N,

  Z :: 0..N, % number of fixpoints in x

  fix_points(Z, X),
  Z #= 4,

  Vars = X ++ [Z],
  solve(Vars),

  println(x=X),
  println(z=Z),
  nl,
  fail,
  
  nl.

go => true.

%
% Also using subcircuit
%
go2 ?=>
  N = 7,

  X = new_list(N),
  X :: 1..N,

  Z :: 0..N, % number of fixpoints in x

  fix_points(Z, X),
  Z #= 6,

  Vars = X ++ [Z],
  solve(Vars),

  println(x=X),
  println(z=Z),
  nl,
  fail,
  
  nl.

go2 => true.



%
% A is the number of fix_points in the list X
%
fix_points(A, X) =>
    A #= sum([X[I] #= I : I in 1..X.len]).