In Haskell, how to reorder multi kinded types

Question

Say I have a type of kind l :: * -> * -> *, so I need to apply 2 types for example a, and b to get a simple type l a b.

How can I map the type l :: * -> * -> * into a new type m(l) :: * -> * -> * where m(l) b a means the same as l a b for every a,b ? Here a,b are not constants. Is it possible? Is it wrong to think of that?

Answer 1

type M l a b = l b a 

newtype M l a b = M (l b a)

Or without taking l as parameter

data L a b = ... 

newtype M a b = M (L b a) 

type M a b = L b a

Edit:

type M l a b = l b a 

data L a b = L (a Int) (b Int)

type Z = M L Maybe []

Moreover, you can give explicit kind signatures too

type M  (l :: k1 -> k2 -> *) (a :: k2) (b :: k1) = l b a