Mapping one list to another (in Haskell, + abstract solution) - 'map reduce'?

Say we have a list of coordinates like:

(1,2)

(0,3)

(4,1)

(0,3)

(-2,3)

(6,5)

And we wanted to result in the following list, which is defined as the summation of each consecutive coordinates. (Sorry bad definition) like so:

(1,5)

(4,4)

(4,4)

(-2,6)

(4,8)

So there exists a set A = (a,b,c,...,n) where a,b,c,...,n are coordinates in R^2.

There exists a function f such that f(A) = B = (a+b,b+c,c+d,...,n-1+n).

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How would you write something like that in a functional la开发者_高级运维nguage like Haskell? A program that applies f to a given A to give B.

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You can use zip to zip the list with its tail, you get pairs of pairs like [((1,2), (0,3)), ((0,3),(4,1)), ...]. Then you can use map to replace each pair of pairs with its sum. Or you can use zipWith which is basically zip + map in one function, except the function given to zipWith has type a -> b -> c, not (a,b) -> c:

summedCoords = zipWith (\ (a,b) (c,d) -> (a+c, b+d)) coords (tail coords)

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You can write a generic function like this

g:: (a -> a -> b) -> [a] -> [b]
g f (x1:x2:xs) = (f x1 x2):(g (x2:xs))
g _ (x1:[]) = []

and pass it your add function

f = g f' where 
    f' (a,b) (a',b') = (a+a', b+b')