> 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/340-lambda-calculi/combinators/combinators2.md).

# Combinators

* Combinator Birds: Index of combinators with SKI equivalents

  <https://www.angelfire.com/tx4/cus/combinator/birds.html>

Combinators are lambda abstractions without free variables, that is, closed lambda terms.

The **identity** function returns whatever argument it is applied to: $$\quad\ \lambda x.x$$

**Self application** function applies its argument to its argument:\
$$\quad\ \lambda f.ff$$