The lambda calculus is Turing-complete, so the following language is sufficient to encode any computable function:

exp ::= var | (lambda (var) exp) | (exp exp)

Check out

http://matt.might.net/articles/church-encodings-demo-in-sche...

To see how to build numbers, booleans, lists, conditionals and recursion out of pure lambdas.

Even cooler is that these tricks work in languages like JavaScript too:

http://matt.might.net/articles/implementation-of-recursive-f...