Haskell - Various factorials P32333

Write 8 essentially diferent functions that compute the factorial of a natural number in Haskell. You can use recursion, final recursion, no recursion, guards, if then else, map, folds, infinite lists...

Specification

You should define the following functions:

    fact1 :: Integer -> Integer
    fact2 :: Integer -> Integer
    fact3 :: Integer -> Integer
    fact4 :: Integer -> Integer
    fact5 :: Integer -> Integer
    fact6 :: Integer -> Integer
    fact7 :: Integer -> Integer
    fact8 :: Integer -> Integer