Formal methods and proof
Establish precisely scoped correctness guarantees
Formal methods express systems and required properties mathematically and establish properties through proofs or exhaustive analysis of a formal model. Theorem proving checks logical derivations; model checking explores a specified state space. Refinement connects abstract specifications with implementations. Guarantees depend on specification adequacy, model boundaries and trusted tools, rather than on statistical sampling.
Use them when failures are costly or universal properties matter, and the system can be specified with sufficient precision and an available proof or state-exploration approach can handle its complexity.
Strengths
- Can cover all behaviours admitted by the formal model
- Makes assumptions and obligations explicit
Limitations
- Specification errors remain possible
- State explosion or proof maintenance can be expensive
Know the boundary
A proof concerns the stated properties under its assumptions; it is not a guarantee against every operational failure.