Nested composition of functors with a type index tracking nesting.

data Flat (x :: * -> *) data Nest (o :: *) (i :: * -> *) data Nested fs a where Flat :: f a -> Nested (Flat f) a Nest :: Nested fs (f a) -> Nested (Nest fs f) a

A Nested fs a is the composition of all the layers mentioned in fs, applied to an a. Specifically, the fs parameter is a sort of snoc-list holding type constructors of kind (* -> *). The outermost layer appears as the parameter to Flat; the innermost layer appears as the rightmost argument to the outermost Nest. For instance:

 [Just ['a']] :: [Maybe [Char]] Flat [Just ['a']] :: Nested (Flat []) (Maybe [Char]) Nest (Flat [Just ['a']]) :: Nested (Nest (Flat []) Maybe) [Char] Nest (Nest (Flat [Just ['a']])) :: Nested (Nest (Nest (Flat []) Maybe) []) Char