Getting Alloy to find the largest answer for particular sets

Question

I'm trying to see if I can get Alloy to return the largest possible answer for a particular set. So, in this example, I would like the answers x={}, x=A, and x=B to not be generated by the model finder.

abstract sig X{}
one sig A extends X{}
one sig B extends X{}

pred(x: set X) {
  x in A + B 
}

I have tried something along the lines of:

pred(x: set X) {
    x in A + B and 
    no y : set X |
        y in A + B and #(y) > #(x)
}

but I get an error that analysis is not possible since it requires higher-order quantification.

I was wondering if there is a possible (or simpler) way to do this?

Answer 1

Alloy does not currently have any built-in functionality to produce maximal or minimal solutions. And yes, you're right that specifying that a solution is maximal generally requires higher order quantification. However, you can ensure that the solution is at least locally maximal with a first order quantification:

    pred p (x: set X) {...}

    pred locally_maximal_p (x: set X) {
      p(x)
      no e: X - x | p(x + e)
      }