Type class and dependent types

Question

First off, I don't know how to properly label my problem. This might also be the reason why I didn't find helpful resources. Any hints are highly appreciated.

trait Context[T]
{
    self =>

    trait Rule
    {
        def apply( value: T ): Boolean
    }

    implicit class RichRule[A <: Rule]( a: A )
    {
        def and[B <: Rule]( b: B ): and[A, B] = self.and( a, b )
        def or[B <: Rule]( b: B ): or[A, B] = self.or( a, b )
    }

    sealed trait Group[A <: Rule, B <: Rule] extends Rule
    {
        def a: A

        def b: B

        override def apply( value: T ) = ???
    }

    case class and[A <: Rule, B <: Rule]( a: A, b: B ) extends Group[A, B]
    case class or[A <: Rule, B <: Rule]( a: A, b: B ) extends Group[A, B]
}

Given the above code, I can now define and chain Rules s in this fashion:

new Context[String]
{
    class MyRule extends Rule
    {
        override def apply( value: String ) = true
    }

    case class A() extends MyRule
    case class B() extends MyRule

    val x1: A and B or A = A() and B() or A()
}

This works as I intended but now comes the tricky part. I want to introduce a Type Class Combination that explains how to join two rules.

trait Combination[-A <: Rule, -B <: Rule]
{
    type Result <: Rule

    def combine( a: A, b: B ): Result
}
trait AndCombination[-A <: Rule, -B <: Rule] extends Combination[A, B]
trait OrCombination[-A <: Rule, -B <: Rule] extends Combination[A, B]

This Type Class should now be passed with the operators.

implicit class RichRule[A <: Rule]( a: A )
{
    def and[B <: Rule]( b: B )( implicit c: AndCombination[A, B] ): and[A, B] = ???
    def or[B <: Rule]( b: B )( implicit c: OrCombination[A, B] ): or[A, B] = self.or( a, b )
}

Which is still working after some tweaks.

implicit val c1 = new Combination[MyRule, MyRule]
{
    type Result = MyRule

    def combine( a: A, b: B ): MyRule = a
}

val x: A and B = A() and B()

But if it gets more complicated, things are falling apart.

A() and B() and A()

Will raise an implicit missing error: Combination[and[A, B], A] is missing. But I want it to use the result of the implicit combination of and[A, B] ( type Result = MyRule ) which it already knows how to handle ( Combination[and[A, B]#Result, A] ).

It is important for me to keep the type information of combined rules val x: A and B or A , folding them together to a final result type is easy, but not what I want.

This is as close as I could get, it fails compilation, though.

trait Context[T]
{
    self =>

    trait Rule

    trait Value extends Rule

    trait Group[A <: Rule, B <: Rule] extends Rule
    {
        def a: A

        def b: B

        implicit val resolver: Resolver[_ <: Group[A, B]]
    }

    case class and[A <: Rule, B <: Rule]( a: A, b: B )( implicit val resolver: Resolver[and[A, B]] ) extends Group[A, B]

    implicit class RichRule[A <: Rule]( a: A )
    {
        def and[B <: Rule]( b: B )( implicit resolver: Resolver[and[A, B]] ) = self.and[A, B]( a, b )
    }

    trait Resolver[-A <: Rule]
    {
        type R <: Value

        def resolve( a: A ): R
    }
}

object O extends Context[String]
{
    implicit val c1 = new Resolver[A and A]
    {
        override type R = A

        override def resolve( a: O.and[A, A] ) = ???
    }

    implicit def c2[A <: Value, B <: Value, C <: Value]( implicit r1: Resolver[A and B] ) = new Resolver[A and B and C]
    {
        override type R = C

        override def resolve( a: A and B and C ): C =
        {
            val x: r1.R = r1.resolve( a.a )
            new c2( x )
            ???
        }
    }

    class c2[A <: Value, B <: Value]( val a: A )( implicit r2: Resolver[A and B] ) extends Resolver[A and B]
    {
        override type R = B

        override def resolve( a: O.and[A, B] ) = a.b
    }

    case class A() extends Value

    val x: A and A and A = A() and A() and A()
}

Answer 1

The reason while your code can't compile is that at the instruction

 new c2( x )

The compiler need to resolve a implicit r2: Resolver[A and B] from x and the only type information available is the type of x , which is r1.R .

This sort of problems requires making more type information available to the compiler and adding some implicit parameter. When you require a Resolver[A and B] , you can't use its R type to resolve another Resolver[r1.R and C] .

type ResolverAux[-A<:Rule,B] = Resolver[A] { type R = B }

With this available, you can rewrite the signature of your c2

implicit def c2[A <: Value, B <: Value, C <: Value,D<:Value]( implicit r1: ResolverAux[A and B,D], r2:Resolver[D and C] ):Resolver[A and B and C] = new Resolver[A and B and C]
  {
    override type R = C

    override def resolve( a: A and B and C ): C =
    {
      val x: r1.R = r1.resolve( a.a )
      new c2[r1.R,C]( x )
      ???
    }
  }

Notice that by using the type alias and introducing an additional generic parameter, I can express the relation r1.R1 = D which is then used to resolve the second implicit r2