You can't. No useful program is stateless. Only examples and proofs-of-concept can be purely functional. The lambda calculus is a way to define math in the fun

You can't. No useful program is stateless. Only examples and proofs-of-concept can be purely functional. The lambda calculus is a way to define math in the functional style. Guess what? It needs state passed in to work. The names and orders of the integers must be passed in and held in a "state" in order to do anything useful. Since functional programming is centered around the concepts from the lambda calculus, this implies that all functional programs must have some "state" somewhere in order to start or do useful work.