% 
% Global constraint all_min_dist in MiniZinc.
% 
% From Global Constraint Catalogue
% http://www.emn.fr/x-info/sdemasse/gccat/sec4.2.html
% """
% Enforce for each pair (vari, varj)​ of distinct variables of the collection VARIABLES that 
% |vari - varj| >= MINDIST.
% 
% Example
%  (2, <5, 1, 9, 3>)
% 
% The all_min_dist constraint holds since the following expressions 
% |5-1|, |5-9|, |5-3|, |1-9|, |1-3|, |9-3| are all greater than or equal to the first 
% argument MINDIST = 2 of the all_min_dist constraint.
% """

% 
% 
% Model created by Hakan Kjellerstrand, hakank@bonetmail.com
% See also my MiniZinc page: http://www.hakank.org/minizinc

% include "globals.mzn"; 

int: n = 4;
array[1..n] of var 1..9: x;
var 0..9: c;

predicate all_min_dist(var int: c, array[int] of var int: x) =
  forall(i, j in 1..n where i != j) (
    abs(x[i]-x[j]) >= c
  )
;

solve satisfy;

constraint
  x = [5,1,9,3]
  /\
  all_min_dist(c, x)
  /\
  c = 2

;