discover-formal

SMT solvers automate formal verification by encoding algorithm properties as logical constraints, then checking satisfiability to prove correctness or find counterexamples. Z3 handles complex constraint problems across integers, reals, and bit-vectors, reducing manual proof effort in critical systems.

SAT solving decides propositional logic satisfiability using Boolean variables; SMT extends this to theories like arithmetic and arrays, enabling direct reasoning about program values and constraints. SMT solvers handle richer verification problems SAT cannot express directly.

Lean provides machine-checked proofs for properties that testing cannot guarantee hold universally. Use Lean when you need mathematical certainty for safety-critical algorithms, type system properties, or correctness claims testing alone cannot validate.

Constraint satisfaction models express program invariants and requirements as logical formulas over variables with domains and constraints. Solvers then search systematically for solutions or prove infeasibility, automating detection of design flaws before implementation.

Formal methods scale through abstraction, modular verification, and SMT solver automation on specific critical components rather than entire systems. Organizations apply them to security kernels, financial engines, and protocol correctness where failure cost justifies proof investment.

Formal verification requires clear specifications of intended behavior, comfort with mathematical logic notation, and knowledge of your target tool's input language (Z3 syntax, Lean tactics, or SMT-LIB). Start with small algorithms before scaling to complex systems.