The other day, I accidentally came up with this:

{-# LANGUAGE RankNTypes #-}

type Either x y = forall r. (x -> r) -> (y -> r) -> r

left :: x -> Either x y
left x f g = f x

right :: y -> Either x y
right y f g = g y

This is one example; it seems that just about any algebraic type can be encoded this way. I presume that somebody else has thought of this before. Does it have a name?

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