I'm suspicious of the theorem proving example. I thought Z3 could fail to return sat or unsat, but he is assuming that if it's not sat the theorem must be proven
No I think it's fine. On another note, I have proven Fermat's Last Theorem with z3 using this setup :) and it goes faster if you reduce a variable called "timeout" for some reason!
from z3 import *
s = Solver()
s.set("timeout", 600)
a = Int('a')
b = Int('b')
c = Int('c')
s.add(a > 0)
s.add(b > 0)
s.add(c > 0)
theorem = a ** 3 + b ** 3 != c ** 3
if s.check(Not(theorem)) == sat:
print(f"Counterexample: {s.model()}")
else:
print("Theorem true")...Whoops. Yup, SMT solvers can famously return `unknown` on top of `sat` and `unsat`. Just added a post addendum about the mistake.
For the curious, solvers like z3 are used in programming languages to verify logic and constraints. Basically it can help find logic issues and bugs during compile time itself, instead of waiting for it to show up in runtime.
https://en.wikipedia.org/wiki/Satisfiability_modulo_theories...
Like in the Dafny pogramming language. Cfr. https://www.youtube.com/watch?v=oLS_y842fMc
The concept is called static analysis.
Seems adjacent, with some overlap.
in theory that's what a compiler is - a thin wrapper over a SAT solver. in practice most compilers just use heuristics <shrug>.
I was expecting a Z3 computer from Germany.