interface (
  Ordered-Comparator-Type [Meta-Type (
    supertypes « (Equality-Comparator-Type),
    instance « (
      receives « (
        [less-than? (first item-type, second item-type)] (
          [replies Boolean] «
            [¬[equal? (first « first, second « second)] ∧
             ¬[greater-than? (first « first, second « second)]]
        ),
        [greater-than? (first item-type, second item-type)] (
          [replies Boolean] «
            [¬[equal? (first « first, second « second)] ∧
             ¬[less-than? (first « first, second « second)]]
        )
        // instance types must override either equal or not-equal
        // and either less-than or greater-than
      ),
      operators « (
        [[left item-type] < [right item-type]] « 
          [less-than? (first « left, second « right)],
        [[left item-type] ≤ [right item-type]] « 
          [[left < right] ∨ [left = right]]
        [[left item-type] > [right item-type]] « 
          [greater-than? (first « left, second « right)],
        [[left item-type] ≥ [right item-type]] « 
          [[left > right] ∨ [left = right]]
      )
    )
  )],

  Ordered-Type [Meta-Type (
    supertypes (Ordered-Comparator-Type, Equality-Type)
  )]
)