A while ago I wrote a Brainfuck interpreter in lambda calculus. I abused the Clojure macro system to make my job a little easier, and of course, I wrapped it in an interface that could do IO, but this does compile to a single pure lambda calculus function which takes a (church encoded) brainfuck program and input string and returns an output string.

https://github.com/MichaelBlume/lambdafuck/blob/master/src/l...