Question

I need to define this function called total.

total :: (Int -> Int) -> Int -> Int

so that the total f is the function which at value n gives the sum
f0 + f1 + …. + fn

Thanks for any help! Please.

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According to the book as an example I found out about function composition that:

twice f = (f . f)   

Here, f is a function, and the result is f composed with itself. For this to work, it needs to have the same input and output type. So we have

twice :: (a -> a) -> a -> a

This states that twice takes one argument, a function of type (a -> a), and returns a result of the same type. For instance, if successor is the function to add one to an integer,

successor :: Int -> Int
successor n = n + 1     
then
(twice successor) 12 ->(successor . successor) 12 
-> successor (successor 12) -> 14

Answer 1

If I understand your question correctly, the following should be fine

total f n = sum [ f i | i <- [0..n] ] 

However I guess you’ll learn more if you define the function recursively. What should total at n=0 return? Well: That’s, by your definition f 0. I.e.

total f 0 = f 0

• Now what about n=1? That’s total f 1 = f 1 + total f 0 == f 1 + f 0.
• For n=2: total f 2 == f 2 + total f 1.
• For n in general?

See the pattern? You can write this into plain Haskell.