Editing Operational semantics (section)

== Comparison ==
There are a number of distinctions between small-step and big-step semantics that influence whether one or the other forms a more suitable basis for specifying the semantics of a programming language.

Big-step semantics have the advantage of often being simpler (needing fewer inference rules) and often directly correspond to an efficient implementation of an interpreter for the language (hence Kahn calling them "natural".) Both can lead to simpler proofs, for example when proving the preservation of correctness under some [[program transformation]].<ref name="leroy-coinductivebigstep">[[Xavier Leroy]]. "Coinductive big-step operational semantics".</ref>

The main disadvantage of big-step semantics is that non-terminating ([[divergence (computer science)|diverging]]) computations do not have an inference tree, making it impossible to state and prove properties about such computations.<ref name="leroy-coinductivebigstep" />

Small-step semantics give more control over the details and order of evaluation. In the case of instrumented operational semantics, this allows the operational semantics to track and the semanticist to state and prove more accurate theorems about the run-time behaviour of the language. These properties make small-step semantics more convenient when proving [[type soundness]] of a type system against an operational semantics.<ref name="leroy-coinductivebigstep" />