Type-safe rectangular multidimensional array type

Question

How do you represent a rectangular 2-dimensional (or multidimensional) array data structure in Scala?

That is, each row has the same length, verified at compile time, but the dimensions are determined at runtime?

Seq[Seq[A]] has the desired interface, but it permits the user to provide a "ragged" array, which can result in a run-time failure.

Seq[(A, A, A, A, A, A)] (and similar) does verify that the lengths are the same, but it also forces this length to be specified at compile time.

Example interface

Here's an example interface of what I mean (of course, the inner dimension doesn't have to be tuples; it could be specified as lists or some other type):

// Function that takes a rectangular array
def processArray(arr : RectArray2D[Int]) = {
    // do something that assumes all rows of RectArray are the same length
}

// Calling the function (OK)
println(processArray(RectArray2D(
    ( 0,  1,  2,  3),
    (10, 11, 12, 13),
    (20, 21, 22, 23)
)))
// Compile-time error
println(processArray(RectArray2D(
    ( 0,  1,  2,  3),
    (10, 11, 12),
    (20, 21, 22, 23, 24)
)))

Answer 1

This is possible using the Shapeless library's sized types:

import shapeless._

def foo[A, N <: Nat](rect: Seq[Sized[Seq[A], N]]) = rect

val a = Seq(Sized(1, 2, 3), Sized(4, 5, 6))
val b = Seq(Sized(1, 2, 3), Sized(4, 5))

Now foo(a) compiles, but foo(b) doesn't.

This allows us to write something very close to your desired interface:

case class RectArray2D[A, N <: Nat](rows: Sized[Seq[A], N]*)

def processArray(arr: RectArray2D[Int, _]) = {
  // Run-time confirmation of what we've verified at compile-time.
  require(arr.rows.map(_.size).distinct.size == 1)
  // Do something.
}

// Compiles and runs.
processArray(RectArray2D(
  Sized( 0,  1,  2,  3),
  Sized(10, 11, 12, 13),
  Sized(20, 21, 22, 23)
))

// Doesn't compile.
processArray(RectArray2D(
  Sized( 0,  1,  2,  3),
  Sized(10, 11, 12),
  Sized(20, 21, 22, 23)
))

Answer 2

Using encapsulation to ensure proper size.

final class Matrix[T]( cols: Int, rows: Int ) {
  private val container: Array[Array[T]] = Array.ofDim[T]( cols, rows )
  def get( col: Int, row: Int ) = container(col)(row)
  def set( col: Int, row: Int )( value: T ) { container(col)(row) = value } 
}