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{{Short description|Category of formal programming language semantics}}
{{Semantics}}'''Operational semantics''' is a category of [[Formal language|formal programming language]] [[Semantics (computer science)|semantics]] in which certain desired properties of a program, such as correctness, safety or security, are [[formal verification|verified]] by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms ([[denotational semantics]]). Operational semantics are classified in two categories: '''structural operational semantics''' (or '''small-step semantics''') formally describe how the ''individual steps'' of a [[computation]] take place in a computer-based system; by opposition '''natural semantics''' (or '''big-step semantics''') describe how the ''overall results'' of the executions are obtained. Other approaches to providing a [[formal semantics of programming languages]] include [[axiomatic semantics]] and [[denotational semantics]].▼
{{Semantics}}
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The operational semantics for a programming language describes how a valid program is interpreted as sequences of computational steps. These sequences then ''are'' the meaning of the program. In the context of [[functional programming]], the final step in a terminating sequence returns the value of the program. (In general there can be many return values for a single program, because the program could be [[Nondeterministic algorithm|nondeterministic]], and even for a deterministic program there can be many computation sequences since the semantics may not specify exactly what sequence of operations arrives at that value.)▼
▲The operational semantics for a [[programming language]] describes how a valid program is interpreted as sequences of computational steps. These sequences then ''are'' the meaning of the program. In the context of [[functional programming]], the final step in a terminating sequence returns the value of the program. (In general there can be many return values for a single program, because the program could be [[Nondeterministic algorithm|nondeterministic]], and even for a deterministic program there can be many computation sequences since the semantics may not specify exactly what sequence of operations arrives at that value.)
Perhaps the first formal incarnation of operational semantics was the use of the [[lambda calculus]] to define the semantics of [[Lisp (programming language)|Lisp]].<ref>{{Cite web |title=Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I |last=McCarthy |first=John |author-link=John McCarthy (computer scientist) |url=http://www-formal.stanford.edu/jmc/recursive.html |access-date=2006-10-13 |url-status=dead |archive-url=https://web.archive.org/web/20131004215327/http://www-formal.stanford.edu/jmc/recursive.html |archive-date=2013-10-04}}</ref> [[Abstract machine]]s in the tradition of the [[SECD machine]] are also closely related.
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