Temporary Variables in forall scope

[SunandanAdhikary]

I am stuck with a forall statement. Found this answer useful. So just wanted to know, is there any way to define a temporary variable to use in the forall scope like we do in z3 using let keyword? Because if there are lots of variables with long expressions, it is difficult to parse for z3py it seems!

Yeah, I don't think there's anything like ((y Int)) in the Python API (when creating your forall); this is because Python (not Z3!) needs to resolve the symbols you want to use inside of your quantification. This is 100% a parse-time thing and not a Z3 limitation.

Your example is something like:

from z3 import *

s = Solver()

z = Int("z")
y = Int("y")

s.add(ForAll([y], Implies(And(y > -5, y < 5), y + z > 10)))

print(s.sexpr())

Originally posted by @andrewvaughanj in #5044 (comment)

[aytey]

You don't have to write the constraint for ForAll "inline"; you can totally do something like:

from z3 import *


def my_fun(y, z):
    return Implies(And(y > -5, y < 5), y + z > 10)


s = Solver()

z = Int("z")
y = Int("y")

s.add(ForAll([y], my_fun(y, z)))

print(s.sexpr())

I think in Z3 parlance, my_fun is called a "generator expression" -- that is, it a function that generates further Z3 expressions.

[SunandanAdhikary]

So I can write anything in place of Implies... in the function definition? Like we normally do in python? And reuse that?

[aytey]

Yes, as long as "normally do" returns a (self-contained) Z3 expression.

[SunandanAdhikary]

Understood. Thank you.