> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/600-toc/624-semantics/operational-semantics.md).

# Operational semantics

math :: theory of computation :: terms

**Operational semantics**, whereby the execution of the language is described directly (rather than by translation).

Operational semantics loosely corresponds to interpretation, although again the "implementation language" of the interpreter is generally a mathematical formalism.

Operational semantics may define an abstract machine (such as the SECD machine), and give meaning to phrases by describing the transitions they induce on states of the machine.

Alternatively, as with the pure lambda calculus, operational semantics can be defined via syntactic transformations on phrases of the language itself.