IMPLICATION
Proofs replace tests. And they're free.
Tests prove something worked for specific inputs. Proofs prove something works for all inputs. Tests need maintenance. Proofs regenerate automatically.
Because specifications are formal, proofs come free.
The comparison
| Tests | Proofs | |
|---|---|---|
| Coverage | Sampled inputs | All inputs |
| Certainty | Probabilistic | Mathematical |
| Time | Hours (10K tests) | Seconds |
| Maintenance | Constant | Zero |
| Edge cases | Must think of them | All covered |
| Flaky? | Yes | Never |
Why proofs are free
When specifications are formal—written in a language with precise semantics—mathematical analysis becomes possible. The system can:
Prove termination
Guarantee the specification will complete (no infinite loops)
Prove determinism
Same input always produces same output
Prove bounds
Values stay within specified limits (e.g., discount ≤ 15%)
Prove isolation
Changes to one rule don't affect unrelated rules
Prove equivalence
Two specifications produce identical behavior
What this means in practice
40% test reduction
Regression tests that just verify "nothing changed" become unnecessary. Proofs cover that.
Zero test maintenance
Change the specification, proofs regenerate automatically. No test updates needed.
No flaky tests
Proofs either pass or fail. Deterministically. Every time. No more "re-run and hope."
Faster pipelines
Seconds instead of hours. Deploy more often. Ship more confidently.
Related implications: