Formal methods |
In levels, but can be used for a completely formal development of an implementation (e.g., a program).
=Taxonomy=
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 software development and verification may be used to produce a program in a more formal manner. For example, proofs of properties or Refinement from the formal 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. This can be very expensive and is only practically worthwhile if the cost of mistakes is extremely high (e.g., in critical parts of microprocessor design).
Further information on this is expanded #Uses.
As with the sub-discipline of Formal semantics of programming languages, styles of formal methods may be roughly classified as follows:
=Uses=
Formal methods can be applied at various points through the software development process. (For convenience, we use terms common to the waterfall model, though any development process could be used.)
==Specification==
Formal methods may be used to give a description of the system to be developed, at whatever level(s) of detail desired. This formal description can be used to guide further development activities (see following sections); additionally, it can be used to verify that the requirements for the system being developed have been completely and accurately specified.
The need for formal specification systems has been noted for years. In the ALGOL 60 Report, John Backus presented a formal notation for describing programming language syntax (later named Backus normal form (BNF)); Backus also described the need for a notation for describing programming language semantics. The report promised that a new notation, as definitive as BNF, would appear in the near future; it never appeared.
==Development==
Once a formal specification has been developed, the specification may be used as a guide while the concrete system is developed (i.e. realized in software and/or hardware). Examples:
==Verification==
Once a formal specification has been developed, the specification may be used as the basis for mathematical proof properties of the specification (and hopefully by inference the developed system).
===Human-Directed Proof===
Sometimes, the motivation for proving the correctness of a system is not the obvious need for re-assurance of the correctness of the system, but a desire to understand the system better. Consequently, some proofs of correctness are produced in the style of , using a level of informality common to such proofs. A good proof is one which is readable and understandable by other human readers.
Critics of such approaches point out that the ambiguity inherent in natural language allows errors to be undetected in such proofs; often, subtle errors can be present in the low-level details typically overlooked by such proofs. Additionally, the work involved in producing such a good proof requires a high level of mathematical sophistication and expertise.
===Automated Proof===
In contrast, there is increasing interest in producing proofs of correctness of such systems by automated means. Automated techniques fall into two general categories:
Neither of these techniques work without human assistance. Automated theorem provers usually require guidance as to which properties are interesting enough to pursue; model checkers can quickly get bogged down in checking millions of uninteresting states if not given a sufficiently abstract model.
Proponents of such systems argue that the results have greater mathematical certainty than human-produced proofs, since all the tedious details have been algorithmically verified. The training required to use such systems is also less than that required to produce good mathematical proofs by hand, making the techniques accessible to a wider variety of practitioners.
Critics note that such systems are like oracles: they make a pronouncement of truth, yet give no explanation of that truth. There is also the problem of verifying the verifier ; if the program which aids in the verification is itself unproven, there may be reason to doubt the soundness of the produced results.
=Criticisms=
In addition to the internal criticisms mentioned above, the field of formal methods as a whole has its critics. At the current state of the art, proofs of correctness, whether handwritten or computer-assisted, need significant time (and thus money) to produce, with limited utility other than assuring correctness. This makes formal methods more likely to be used in fields where the benefits of having such proofs, or the danger in having undetected errors, makes them worth the resources. Example: in aerospace engineering, undetected errors may cause death, so formal methods are more popular than in other application areas.
At times, proponents of formal methods have claimed that their techniques would be the silver bullet to the software crisis. Of course, there is no silver bullet for software development, and some have written off formal methods due to those overstated, overreaching claims.
=Related topics=
=See also=
=References=
=External links=
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