map length (tiers :: [[ ()->Nat ]])  =  [1,1,1,1,1,1,...]

length (list :: [ ()->Nat ])  =  Infinity

allUnique (list :: [ ()->Nat ])  =  True

ratioRepetitions (list :: [ ()->Nat ])  =  0 % 1

tiers :: [()->Nat]  =
  [ [ \x -> case x of
              () -> 0
    ]
  , [ \x -> case x of
              () -> 1
    ]
  , [ \x -> case x of
              () -> 2
    ]
  , [ \x -> case x of
              () -> 3
    ]
  , [ \x -> case x of
              () -> 4
    ]
  , [ \x -> case x of
              () -> 5
    ]
  , ...
  ]