def find_new_bindings(bindings, e1, e2):
  e1 = normalize(bindings, e1)

  progress = false

  if e1 is Var:
      bindings.add(e1, e2)
      return true

  if (e1 is Apply) and (e2 is Apply):
    progress |= find_new_bindings(bindings, e1.head, e2.head)
    progress |= find_new_bindings(bindings, e1.arg, e2.arg)
    return progress

  if (e1 is Multiname) and (e2 is Multiname):
    if not intersects(e1, e2):
        error "doesnt match"

  return false

def normalize(bindings, e):
  if e in bindings:
    return bindings[e]
  return e