Constructing pairs using functions as in System F, instead of built-in products

system_f_product.hs

data A = A1 | A2 deriving Show
data B = B1 | B2 | B3 deriving Show

type PairAB x = (A -> B -> x) -> x

pairAB :: A -> B -> PairAB x
pairAB a b g = g a b

fstAB :: PairAB A -> A -- ((A -> B -> A) -> A) -> A
fstAB p = p (\x y -> x)

sndAB :: PairAB B -> B -- ((A -> B -> B) -> B) -> B
sndAB p = p (\x y -> y)

type PairAny a b x = (a -> b -> x) -> x

pairAny :: a -> b -> PairAny a b x
pairAny a b g = g a b

fstAny :: PairAny a b a -> a
fstAny p = p (\x y -> x)

sndAny :: PairAny a b b -> b
sndAny p = p (\x y -> y)