You can do this pretty cleanly with a recursive function that traverses the tree and expands ambiguities:
sealed trait Term
case class App(f: Term, x: Term) extends Term
case class Var(s: String) extends Term
case class Amb(a: Term, b: Term) extends Term
def det(term: Term): Stream[Term] = term match {
case v: Var => Stream(v)
case App(f, x) => det(f).flatMap(detf => det(x).map(App(detf, _)))
case Amb(a, b) => det(a) ++ det(b)
}
Note that I'm using a sealed trait instead of an abstract class in order to take advantage of the compiler's ability to check exhaustivity.
It works as expected:
scala> val app = App(Var("f"), Amb(Var("x"), Amb(Var("y"), Var("z"))))
app: App = App(Var(f),Amb(Var(x),Amb(Var(y),Var(z))))
scala> det(app) foreach println
App(Var(f),Var(x))
App(Var(f),Var(y))
App(Var(f),Var(z))
If you can change the Term
API, you could more or less equivalently add a def det: Stream[Term]
method there.