Building variations of nested case classes - scala

Question

So I got something like this:
abstract class 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 //ambiguity
And a Term may look like this:
App(Var(f),Amb(Var(x),Amb(Var(y),Var(z))))
So what I need is all variations that are indicated by the Amb class.
This is used to represent a ambiguous parse forest and I want to type check each possible variation and select the right one.
In this example I would need:
App(Var(f),Var(x))
App(Var(f),Var(y))
App(Var(f),Var(z))
Whats the best way to create these variations in scala?
Efficiency would be nice, but is not really requirement.
If possible I like to refrain from using reflection.

Answer 1

Scala provides pattern matching solve these kinds of problems. A solution would look like:
def matcher(term: Term): List[Term] = {
term match {
case Amb(a, b) => matcher(a) ++ matcher(b)
case App(a, b) => for { va <- matcher(a); vb <- matcher(b) } yield App(va, vb)
case v: Var => List(v)
}
}

Answer 2

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.

Answer 3

Since my abstract syntax is fairly large (and I have multiple) and I tried my luck with Kiama.
So here is the version Travis Brown and Mark posted with Kiama.
Its not pretty, but I hope it works. Comments are welcome.
def disambiguateRule: Strategy = rule {
case Amb(a: Term, b: Term) =>
rewrite(disambiguateRule)(a).asInstanceOf[List[_]] ++
rewrite(disambiguateRule)(b).asInstanceOf[List[_]]
case x =>
val ch = getChildren(x)
if(ch.isEmpty) {
List(x)
}
else {
val chdis = ch.map({ rewrite(disambiguateRule)(_) }) // get all disambiguate children
//create all combinations of the disambiguated children
val p = combinations(chdis.asInstanceOf[List[List[AnyRef]]])
//use dup from Kiama to recreate the term with every combination
val xs = for { newchildren <- p } yield dup(x.asInstanceOf[Product], newchildren.toArray)
xs
}
}
def combinations(ll: List[List[AnyRef]]): List[List[AnyRef]] = ll match {
case Nil => Nil
case x :: Nil => x.map { List(_) }
case x :: xs => combinations(xs).flatMap({ ys => x.map({ xx => xx :: ys }) })
}
def getChildren(x: Any): List[Any] = {
val l = new ListBuffer[Any]()
all(queryf {
case a => l += a
})(x)
l.toList
}