libraryDependencies += "io.github.lamdalib" %% "kuram" % "0.1.0-SNAPSHOT"

import kuram.Monoid
// you can access combine alias (|+|) under syntax.
import kuram.syntax.*

// you can access int monoid
import kuram.instances.int.given
// or, if you want to access list, string etc.
// import kuram.instances.string.given
// import kuram.instances.list.given

// or, you can import all givens as follows:
// import kuram.instances.all.given

import kuram.instances.list.given

import Matrix.*

object Matrix {
    type Matrix[A] = List[List[A]]
    
    def apply[A](instance: List[List[A]]): Matrix[A] = instance

    def zero[A: Monoid](row: Int, col: Int): Matrix[A] =
        Matrix(List.fill[A](row, col)(Monoid[A].empty))

    extension [A: Monoid](m1: Matrix[A])
        def +(m2: Matrix[A]): Matrix[A] = apply:
          for (rowLeft, rowRight) <- m1 zip m2 yield
            for (row, col) <- rowLeft zip rowRight yield
              row |+| col
}

def matrixMonoid(row: Int, col: Int): Monoid[Matrix[Int]] = new {
    def empty: Matrix[Int] = Matrix.zero(row, col)
    def combine(a: Matrix[Int], b: Matrix[Int]): Matrix[Int] = a + b
}

@main def start: Unit = 
    val m1 = Matrix(List(List(1, 1), List(7, 3)))
    val m2 = Matrix(List(List(2, 2), List(3, 4)))

    val matrices = List(m1, m2)
    val (row, col) = (2, 2)

    val expected = Matrix(List(List(3, 3), List(10, 7)))
    val obtained = matrices.foldMap(identity)(using matrixMonoid(row, col))

    println(s"Obtained: $obtained\nExpected: $expected")
    assert(obtained == expected, "wrong!")