Contradictory Behaviour of Lambda Functions

Question

Using the following definitions:

lenDigits n = length (show n) factorial n = product [1..n] 

I evaluate the following

Prelude> ((lenDigits . factorial) 199) <= 199 False Prelude> (\i -> ((lenDigits . factorial) i) <= i) 199 True 

What is the reason for such behaviour? As I see it, the first expression is just the same as the second expression with the lambdas reduced.

Answer 1

Because in the first expression the first 199 has type Integer and the second has Int. But in the second expression both have type Int and factorial 199 can't be represented by the type Int.