Formal methods

In computer science, formal methods are mathematically rigorous techniques for the specification, development, analysis, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design. Formal methods employ a variety of theoretical computer science fundamentals, including logic calculi, formal languages, automata theory, control theory, program semantics, type systems, and type theory. Semi-formal methods are formalisms and languages that are not considered fully "formal". It defers the task of completing the semantics to a later stage, which is then done either by human interpretation or by interpretation through software like code or test case generators. Formal methods can be used at a number of levels: Level 0: Formal specification may be undertaken and then a program developed from this informally. This has been dubbed formal methods lite. This may be the most cost-effective option in many cases. Level 1: Formal development and formal verification may be used to produce a program in a more formal manner. For example, proofs of properties or refinement from the specification to a program may be undertaken. This may be most appropriate in high-integrity systems involving safety or security. Level 2: Theorem provers may be used to undertake fully formal machine-checked proofs. Despite improving tools and declining costs, this can be very expensive and is only practically worthwhile if the cost of mistakes is very high (e.g., in critical parts of operating system or microprocessor design). Further information on this is expanded below. As with programming language semantics, styles of formal methods may be roughly classified as follows: Denotational semantics, in which the meaning of a system is expressed in the mathematical theory of domains.