Sofi

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h1 f g x y = f (g x y) x
(a -> b -> c) -> (b -> d -> a) -> b -> d -> c

h2 f x y = f y x
(a -> b -> c) -> b -> a -> c

h3 f g x y = (f x y , g y x)
(a -> b -> c) -> (b -> a -> d) -> a -> b -> (c,d)

h4 f x y = (f x x , f y y)
(a -> a -> b) -> a -> a -> (b,b)

h5 x y z = z y x
a -> b -> (b -> a -> c) -> c

h6 x y z = (x y) (z y)
(a -> b -> c) -> a -> (a -> b) -> c

h7 g h x y = (h x y , g x)
(a -> b) -> (a -> c -> d) -> a -> c -> (d,b)

h8 x y z = y (x z)
(a -> b) -> (b -> c) -> a -> c

h9 x f = f (f x)
a -> (a -> a) -> a