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Formal methods use mathematically defined models, specifications and reasoning techniques to describe and analyze systems. They include writing a formal specification, proving properties through formal verification, exploring a finite model by model checking and deriving information through static program analysis. A method's guarantee is relative to its model and assumptions.

For example, a loop summing an array can maintain the invariant that the current accumulator equals the sum of the entries already visited. Initialization, preservation by one iteration and the exit condition establish the returned sum; a separate termination argument shows that an answer is reached. Arithmetic and array bounds must be specified, since a proof using unbounded integers need not describe overflowing machine arithmetic.^[ref]

Static program analysis derives information about a computer program from its representation and programming language semantics, without executing each concrete input case. An analysis commonly approximates many possible executions at once. Data-flow analysis propagates such information between locations in a control-flow graph.^[ref]

For example, after if c then x=1 else x=2, an analysis can infer that x belongs to $\{1,2\}$ at the join and hence is nonzero. More complicated paths may force a less precise answer. A conservative warning can therefore flag a possible failure that no actual input reaches. The guarantee depends on what the approximation includes: failing to model an external call or integer overflow can invalidate an apparent proof.