Can we merge the interpreters?

sample.scala

// simplified code to give the idea. Starting with 2 DSL, Trades and Http
object Trades {
  sealed trait DSL[A] { def url: String }
  final case class HeartBeat() extends DSL[TradeResult[StatusOk]] 

  type TradesPRG[A] = (DSL :|: FXNil)#Cop[A]
}

object Http {
  sealed trait DSL[A]
  final case class Get(url: String, parameters:  Map[String, List[String]]) extends DSL[Result]
 
  type HttpPRG[A] = (DSL :|: FXNil)#Cop[A]
  val executerInterpreter: Interpreter[HttpPRG, Task] = AsyncHttpInterpreter
  
  // I need this alias for interpreters, see comments below
  type HttpFree[A] = Free[HttpPRG, A]
}

// Now we define an interpreter from Http to AsyncHttp (some code omitted for brevity)
object AsyncHttpInterpreter extends (Http.DSL ~> Task) {
  import Http._

  def apply[A](a: Http.DSL[A]) = a match {
    case Get(url, parameters) => get(url, parameters)
  }
}

// It seems I can't create an interpreter from Trades.DSL to Http.DSL, instead I need to go from Trades.DSL to Http.HttpFree
object TradesHttpInterpreter extends (Trades.DSL ~> Http.HttpFree) {
  import Trades._
  import Http._

  def apply[A](a: Trades.DSL[A]) = a match {
    case o @ HeartBeat() =>
      val x: Free[HttpPRG, Result] = for {
         rsp <- Get(o.url, Map.empty[String, List[String]]).freek[HttpPRG]
      } yield rsp
      x.map(rslt => StatusOk().asInstanceOf[A].right)
  }
}
// To run a program them it seems I can't combine the interpreters I have, but I need to run 2 foldmap in a row 
// (compile fails when trying to compose them)
localProgram
        .foldMap(TradesHttpInterpreter.nat).foldMap(Http.executerInterpreter.nat)
        .runAsync

// Is there any way to combine TradesHttpInterpreter and Http.executerInterpreter in a single interpreter?

it certainly means you want to :
1/ convert result of Http to TradesResult : Trades.DSL ~> Http.DSL ~> TradesResult.DSL
2/ combine Trades.DSL & Http.DSL in your program as a Coproduct Trades.DSL :|: Http.DSL

yes, I see, I was doing it the wrong way around, thanks! you helped a lot! :)