Editing Formal verification (section)

=== Deductive verification ===

Another approach is deductive verification.<ref>{{cite book |title=Deductive Software Verification - The KeY Book: From Theory to Practice |editor-first1 = Wolgang |editor-last1 = Ahrendt |editor-last2 = Beckert| editor-first2 = Bernhard |editor-last3 = Bubel |editor-first3 = Richard |editor-last4 = Hähnle |editor-first4 = Reiner |editor-last5 = Schmitt |editor-first5 = Peter H. | date=2016 |publisher=Springer International Publishing : Imprint: Springer |location=Cham |isbn=978-3-319-49812-6 |edition=1st 2016}}</ref><ref>{{cite book |title=Engineering secure and dependable software systems |editor-last1 = Pretschner |editor-first1 = Alexander |editor-last2 = Müller |editor-first2 = Peter |editor-last3 = Stöckle |editor-first3 =  Patrick |date=2019 |publisher=IOS Press |location=Amsterdam, Netherlands |isbn=978-1-61499-976-8 | chapter = 
Building Deductive Program Verifiers - Lecture Notes}}</ref> It consists of generating from the system and its specifications (and possibly other annotations) a collection of mathematical ''proof obligations'', the truth of which imply conformance of the system to its specification, and discharging these obligations using either [[proof assistant]]s (interactive theorem provers) (such as [[HOL theorem prover|HOL]], [[ACL2]], [[Isabelle (theorem prover)|Isabelle]], [[Rocq (software)|Rocq]] (previously known as ''Coq'') or [[Prototype Verification System|PVS]]), or [[Automated theorem proving|automatic theorem provers]], including in particular [[satisfiability modulo theories]] (SMT) solvers. This approach has the disadvantage that it may require the user to understand in detail why the system works correctly, and to convey this information to the verification system, either in the form of a sequence of theorems to be proved or in the form of specifications (invariants, preconditions, postconditions) of system components (e.g. functions or procedures) and perhaps subcomponents (such as loops or data structures).