Question

I’ve got a good idea of what primitive recursive definitions are, however I still can’t seem to get my head around it.

For example, I can’t seem to explain to myself how to do the following (yet I seem to be able to do it):

Exercise:

Define the function
productIt :: [Int] -> Int
which gives the product of a list of integers, and returns 1 for an empty list; why is this particular value chosen as the result for the empty list?

I (of course) came up with the solution:

productIt :: [Int] -> Int
productIt [] = 1
productIt (x:xs) = x * productIt xs

which works perfectly for the question in the exercise. Yet I still seem to have trouble getting my head around the final line.

Any ideas on how to think this out would be most appreciated.

Answer 1

In English, you could read that final line as:

The product of a list of numbers is the first number times the product of the rest of the numbers. And if there are no numbers, let’s just say the product is 1.

Converting it to English like this usually helps me understand how and why a recursive function works. You could also evaluate it with the Haskell interpreter inside your head:

  productIt [2,3,4]
= 2 * (productIt [3,4])
= 2 * (3 * (productIt [4]))
= 2 * (3 * (4 * (productIt [])))
= 2 * (3 * (4 * (1)))
= 2 * (3 * (4))
= 2 * (12)
= 24