Understanding this matrix transposition function in Haskell

Question

This matrix transposition function works, but I\'m trying to understand its step by step execurtion and I don\'t get it.

    transpose:: [[a]]->[[a]]
    tran         


        

Answer 1

Let's look at what the function does for your example input:

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]]

Note that the order in which I chose to reduce the terms, is not the same as the evaluation order haskell will use, but that does not change the result.

Edit: In response to your edited question:

is this

(map head x)

creating a list of the head elements of each list?

Yes, it is.