could you please define the following functions in haskell and test them. 1)Defi

Question

could you please define the following functions in haskell and test them.

1)Define a Haskell function map2 that takes a list of functions and a list of values and returns the list of results of applying each function in the first list to the corresponding value in the second list.

2)Define a Haskell function fmap that takes a value and a list of functions and returns the list of results from applying each function to the argument value. (For example, fmap 3 [((*) 2), ((+) 2)] yields [6,5].)

3)Define a Haskell function composeList that takes a list of functions and composes them into a single function. (Be sure to give the type signature.)

Explanation / Answer

1. -- Haskell function map2 that takes a list of functions and a list of values and returns the list of results of applying each function in the first list to the corresponding value in the second list.

      map2 :: [(a->b)] ->[a] ->[b]

     map2 funcs args = zipWith (x y -> x $ y ) funcs args

2.-- Haskell function fmap that takes a value and a list of functions and returns the list of results from applying each function to the argument value.

    fmap'' :: a -> [(a->b)] -> [b]

   fmap'' arg funcs = map2 funcs (repeat arg)

3. -- Haskell function composeList that takes a list of functions and composes them into a single function.

     composeList :: [(a->a)] -> (a->a)

    composeList funcs = foldr1 (1 a2-> a1.a2) funcs

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