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

ghci is your friend:

*Main> :t map head
map head :: [[a]] -> [a]
*Main> :t map tail
map tail :: [[a]] -> [[a]]

Even if you don't understand map (a problem you'd want to correct quickly!), the types of these expressions tell much about how they work. The first is a single list taken from a list of lists, so let's feed a simple vector to it to see what happens.

You might want to write

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

but that fails to typecheck:

:1:14:
    No instance for (Num [a])
      arising from the literal `3' at :1:14
    Possible fix: add an instance declaration for (Num [a])
    In the expression: 3
    In the second argument of `map', namely `[1, 2, 3]'
    In the expression: map head [1, 2, 3]

Remember, the argument's type is a list of lists, so

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

Getting a bit more complex

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

Doing the same but with tail instead of head gives

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

As you can see, the definition of transpose is repeatedly slicing off the first “row” with map head x and transposing the rest, which is map tail x.