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z3z3pyquantifiers

Counting number of variables in Z3 quantified formula

I'm trying to collect all the variables in a formula (quantified formula in Z3py). A small example 

w, x, y, z = Bools('w x y z')
fml = And( ForAll(x, ForAll(y, And(x, y))), ForAll(z, ForAll(w, And(z, w))) ) 

varSet = traverse( fml )

The code i use to traverse is 

def traverse(e):
  r = set()
  def collect(e):
    if is_quantifier(e):
      # Lets assume there is only one type of quantifier
      if e.is_forall():
          collect(e.body())
    else:
      if ( is_and(e) ):
          n = e.num_args()
          for i in range(n):
              collect( e.arg(i) )
      if ( is_or(e) ):
          n = e.num_args()
          for i in range(n):
              collect( e.arg(i) )
      if ( is_not(e) ):
          collect( e.arg(0) )
      if ( is_var(e) ):
          r.add( e )
  collect(e)
  return r

And I'm getting: set( [Var(0), Var(1)] ). As i understand this is due to Z3 uses De Bruijn index. Is it possible to avoid this and get the desired set: set( [Var(0), Var(1), Var(2), Var(3)] ).

Solution

  • Your code is correct; there is no Var(2) or Var(3) in this example. There are two top-level quantifiers and the de-Bruijn indices in each of them are 0 and 1. Those two quantifiers do not appear within the body of another quantifier, so there can be no confusion.