How does scanr work? Haskell

Question

I messed around with some of the Haskell features, some of which I understood, and some not.

For example, if we do: scanl (+) 0 [1..3] , I understand the following:

 1. the accumulator is 0 acc = 0 | 2. (+) applied to acc and first el acc = 0 + 1 = 1 | 3. (+) applied to latest acc and snd el acc = 1 + 2 = 3 | 4. (+) applied to latest acc and third acc = 3 + 3 = 6 V 

Now, when we create the list, we get [0, 1, 3, 6] .

But I can’t understand how scanr (+) 0 [1..3] gives me: [6,5,3,0] Maybe scanr works as follows?

 1. the first element in the list is the sum of all other + acc 2. the second element is the sum from right to left (<-) of the last 2 elements 3. the third element is the sum of first 2... 

I do not see if this is a template or not.

Answer 1

scanr corresponds to foldr , which scanl equals foldl . foldr works on the right:

 foldr (+) 0 [1,2,3] = (1 + (2 + (3 + 0))) = (1 + (2 + 3)) = (1 + 5) = 6 

and scanr simply show intermediate results in the sequence: [6,5,3,0] .