F# Multidimensional Array Types

Question

What's the difference between 'a[,,] and 'a[][][]? They both represent 3-d arrays. It makes me write array3d.[x].[y].[z] instead of array3d.[x, y, z].

Why I can't do the following?

> let array2d : int[,] = Array2D.zeroCreate 10 10;;
> let array1d = array2d.[0];;

error FS0001: This expression was expected to have type
    'a []    
but here has type
    int [,]

Answer 1

The difference is that 'a[][] represents an array of arrays (of possibly different lengths), while in 'a[,], represents a rectangular 2D array. The first type is also called jagged arrays and the second type is called multidimensional arrays. The difference is the same as in C#, so you may want to look at the C# documentation for jagged arrays and multidimensional arrays. There is also an excelent documentation in the F# WikiBook.

To demonstrate this using a picture, a value of type 'a[][] can look like this:

0 1 2 3 4
5 6
7 8 9 0 1

While a value of type a[,] will always be a rectangle and may look for example like this:

0 1 2 3
4 5 6 7
8 9 0 1

---

To get a single "line" of a multidimensional array, you can use the slice notation:

let array1d = array2d.[0..0,0..9];;

Slices actually return multidimensional array (in this case, with one dimension equal to 1), so you can write a conversion function that returns 'a[] like this:

let toArray (arr:_[,]) = 
  Array.init arr.Length (fun i -> arr.[0, i])

let array1d = array2d.[0..0,0..9] |> toArray;;