A set of types F[T₁], …, F[Tᵢ], …, F[Tₙ], where F's parameter is invariant, has an universal (∀) upper bound of F[T] for some choice of T where LUB(Tᵢ) <: T <: GLB(Tᵢ) if it exists, and an existential (∃) upper bound of F[T] for some T where GLB(Tᵢ) <: T <: LUB(Tᵢ).
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I find it beautiful that a solution exists in the dual, existential world, when it doesn't exist in the universal world, and that solution is found by calculating the type bounds using categorical duals of the algorithms for the (nonexistent) universal solution.
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