[Haskell-cafe] Why do functions not inherit class when renamed?

I'm not sure I understand what is going on here, but it seems to me that the following assignment of "mult = (*)" causes "mult" to lose out on some of the polymorphic behavior of (*). Is that right? If so, why?

Prelude Data.Function Data.List Data.Char> let sizeMult = (*) `on` length Prelude Data.Function Data.List Data.Char> sizeMult "Duane" "Johnson" 35 Prelude Data.Function Data.List Data.Char> let mult = (*) Prelude Data.Function Data.List Data.Char> let sizeMult2 = mult `on` length

<interactive>:1:26: Couldn't match expected type `Integer' against inferred type `Int' In the second argument of `on', namely `length' In the expression: mult `on` length In the definition of `sizeMult2': sizeMult2 = mult `on` length Prelude Data.Function Data.List Data.Char>

Thanks, Duane Johnson http://blog.inquirylabs.com/