[Haskell-cafe] Deducing a type signature

[R J]

Bird 1.6.3 requires deducing type signatures for the functions "strange" and "stranger."
Are my solutions below correct?
(i)  strange f g = g (f g)
Assume g :: a -> b.  Then f :: (a -> b) -> c.  But since g :: a -> b,f g :: a, so c = a.  Therefore, f :: (a -> b) -> a, and g (f g) :: a.Therefore, strange :: ((a -> b) -> a) -> (a -> b) -> a.
(ii)  stranger f = f f
Assume f :: a -> b.  Since "f f" is well-typed, type unification requiresa = b.  Therefore, f :: a -> a, and stranger :: (a -> a) -> a. 		 	   		  
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