scala-bimodule

Main.scala

object Main {

  abstract class Ab[A] {
    val add: (A, A) => A
    val neg: A => A
  }
  abstract class Ring[R] extends Ab[R] {
    val mul: (R, R) => R
  }
  abstract class Field[F] extends Ring[F] {
    val inv: F => Option[F]
  }

  abstract class Mod[A: Ring, M, B: Ring] extends Ab[M]
  {
    val lact: (A, M) => M
    val ract: (M, B) => M
  }

  type +[M, N] = (M, N)

  implicit def Mod1_+[A: Ring, M, N, B: Ring](implicit Mod_M: Mod[A, M, B], Mod_N: Mod[A, N, B] ): Mod[A, M+N, B] =
    new Mod[A, M+N, B] {
      override val lact: (A, (M, N)) => (M, N) = ???
      override val ract: ((M, N), B) => (M, N) = ???
      override val add: ((M, N), (M, N)) => (M, N) = ???
      override val neg: M + N => M + N = ???
    }

  implicit def Mod2_+[A: Ring, M: Mod[A, ?, B], N: Mod[A, ?, B], B: Ring]: Mod[A, M+N, B] =
    new Mod[A, M+N, B] {
      override val lact: (A, (M, N)) => (M, N) = ???
      override val ract: ((M, N), B) => (M, N) = ???
      override val add: ((M, N), (M, N)) => (M, N) = ???
      override val neg: M + N => M + N = ???
    }

}