Some tests in this directory (in particular, least_and_greatest_closure_A*.dart) check the least and greatest closure of a type. To do this, we examine the results of the UP and DOWN functions. However, we need to be careful because these functions may return a type that was not produced by the least/greatest closure computation itself.

The least and greatest closure of type is defined with respect to a set of type variables. The definitions of UP and DOWN include the following rules:

• UP(T1, T2) = T2 if T1 <: T2
• UP(T1, T2) = T1 if T2 <: T1 ...
• DOWN(T1, T2) = T1 if T1 <: T2
• DOWN(T1, T2) = T2 if T2 <: T1

This means that the two types must not be subtypes of each other. Otherwise, UP and DOWN will return one of the input types directly, which is not what these tests are intended to verify.

Therefore, each test must use two type variables with the same structure (that is, one is simply an alpha-conversion of the other), such that neither is a subtype of the other. This forces UP or DOWN to use the rule that computes the least/greatest closure on both arguments. As a result, we compute UP/DOWN(erasedType, erasedType), which evaluates to erasedType, allowing us to inspect the result produced by the least/greatest closure algorithm.