Distance between points on haskell

We can rename this function to distance2 to specify that it calculates the distance between two points:

distance2 :: Floating a => (a, a) -> (a, a) -> a
distance2 (x1 , y1) (x2 , y2) = sqrt (x'*x' + y'*y')
    where x' = x1 - x2
          y' = y1 - y2

Next we can make use of zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] to iterate concurrently over two lists, and apply a function to the elements. Here we iterate over the list, and its tail. This will thus produce a list of distances. We can make use of sum :: (Num a, Foldable f) => f a -> a to sum up these distances:

distance2 :: Floating a => [(a, a)] -> a
distance [] = 0
distance xa@(_:xs) = sum (zipWith distance2 xa xs)

Firstly, like @WillemVanOnsem, I will rename distance to distance2:

distance2 :: Floating a => (a, a) -> (a, a) -> a
distance2 (x1 , y1) (x2 , y2) = sqrt (x'*x' + y'*y')
    where x' = x1 - x2
          y' = y1 - y2

Next, given a list, a function to split it into pairs:

splitPairs :: [a] -> [(a,a)]
splitPairs (x:y:xs) = (x,y) : (splitPairs (y:xs))
splitPairs _ = error "can’t split into pairs when <2 elements!"

Finally, given a list of points, split it into pairs, calculate the distance between each pair, and add them up:

distance :: Floating a => [(a,a)] -> a
distance = sum . map (uncurry distance2) . splitPairs

Without recursion it would be best to use zipWith and sum functions with the applicative operator <*>.

Prelude> :{
Prelude| dist :: Floating a => [(a, a)] -> a
Prelude| dist = sum . (ds <*> tail)
Prelude|        where ds = zipWith (\f s -> sqrt ((fst f - fst s)^2 + (snd f - snd s)^2))
Prelude| :}
Prelude> dist [(0,0),(2,0),(2,5)]
7.0
Prelude> dist [(1,1),(3,4)]
3.605551275463989