Rank 3 Types function example

Question

I have this Rank 3 Type function definition:

f3 :: ((forall a. a -> a) -> Int) -> Bool -> Bool
f3 .... = ?

and I am struggling to write a simple example for it. Can you help?

Answer 1

f3 :: ((forall a. a -> a) -> Int) -> Bool -> Bool
f3 f b = (f id == 3) && b

f3_ex :: Bool
f3_ex = f3 f True where
   f :: (forall a. a -> a) -> Int
   f g = g 3

Changing the type to be more interesting, as mentioned in the comments:

f4 :: ((forall a. a -> a -> a) -> Int) -> Bool -> Bool
f4 f b = (f const == 3) && b

f4_ex :: Bool
f4_ex = f4 f True where
   f :: (forall a. a -> a -> a) -> Int
   f g = g 3 5


f5 :: ((forall a. a -> a -> a) -> Int) -> Bool -> Bool
f5 f b = f (if b then const else const id) == 42

f5_ex :: Bool
f5_ex = f5 f True where
   f :: (forall a. a -> a -> a) -> Int
   f g = g 3 5 + 39

Here f is essentially of type (Int, Int), the first component given by f const and the other one given by f (const id) or equivalently f (flip const).