statically checked, but still runtime-determined, matrix sizes can be done in Scala. Doing specialized implementations would require bytecode magic, though.

  case class Dim(size: Int)

  trait Matrix[X <: Dim with Singleton, Y <: Dim with Singleton] {
    def *[Z <: Dim with Singleton](other: Matrix[Y, Z]):Matrix[X, Z] = ???
  }

  object Matrix {
    def apply[X <: Dim with Singleton, Y <: Dim with Singleton](x: X, y: Y):Matrix[X,Y] = ???
  }

  val x = Dim(100)
  val y = Dim(readFromFile(...))
  val z = Dim(37)

  val A = Matrix[x.type, y.type](x, y)
  val B = Matrix[y.type, z.type](y, z)

  A * A // compile error
  A * B // ok