transpose:: [[a]]->[[a]]
    transpose ([]:_) = []
    transpose x = (map head x) : transpose (map tail x)

transpose [[1,2,3],[4,5,6],[7,8,9]]

[[1,4,7],[2,5,8],[3,6,9]]

(map head x)

transpose [[1,2,3],[4,5,6],[7,8,9]]
<=>
(map head [[1,2,3],[4,5,6],[7,8,9]]) : (transpose (map tail [[1,2,3],[4,5,6],[7,8,9]]))
<=>
[1,4,7] : (transpose [[2,3],[5,6],[8,9]])
<=>
[1,4,7] : (map head [[2,3],[5,6],[8,9]]) : (transpose (map tail [[2,3],[5,6],[8,9]]))
<=>
[1,4,7] : [2,5,8] : (transpose [[3],[6],[9]])
<=>
[1,4,7] : [2,5,8] : (map head [[3],[6],[9]]) : (transpose (map tail [[3],[6],[9]]))
<=>
[1,4,7] : [2,5,8] : [3, 6, 9] : (transpose [[], [], []])
<=>
[1,4,7] : [2,5,8] : [3, 6, 9] : [] -- because transpose ([]:_) = []
<=>
[[1,4,7],[2,5,8],[3,6,9]]

(map head x)

(map head x) : transpose (map tail x)

[x,y,z,...] : [[a,b,...],[d,e,...],...] = [[x,y,z,...], [a,b,...],[d,e,...],...]

x = [[1,2,3],[4,5,6],[7,8,9]]

map head x = [1,4,7]
map tail x = [[2,3],[5,6],[8,9]]

transpose (map tail x) = [[2,5,8],[3,6,9]]

map head x : transpose (map tail x) =  [1,4,7] : [[2,5,8],[3,6,9]]
                                    = [[1,4,7] ,  [2,5,8],[3,6,9]]

map

*Main> map head [1,2,3]

*Main> map head [[1,2,3]]
[1]

*Main> map head [[1,2,3]]
[1]

*Main> map head [[1,2,3],[4,5,6]]
[1,4]

*Main> map tail [[1,2,3],[4,5,6]]
[[2,3],[5,6]]

map head xxs
map (xs -> head xs) xxs

map head [[1,2,3],[4,5,6],[7,8,9]]
-> map (xs -> head xs) [[1,2,3],[4,5,6],[7,8,9]]
-> [head [1,2,3], head [4,5,6], head [7,8,9]]
-> [1,4,7]