A simple input sample: (lambda x.(x x))(lambda x.(x x)). Or type help to learn more.
Try fix-point combinator: (lambda f. ((lambda x.(f (x x))) (lambda x.(f (x x))))) (lambda x.x)
What is λ Calculus?
λ Calculus is considered as the smallest universal programming language.
The λ calculus is developed as a theory of functions for manipulating functions in a purely syntactic manner.
All functional programming languages can be viewed as syntactic variations of the lambda calculus, so that both their semantics
and implementation can be analysed in the context of the lambda calculus.
Church's Thesis: The effectively computable functions on the positive integers are precisely those functions definable in the pure
lambda calculus (and computable by Turing machines).
The term "thesis" means a conjecture. But since all methods developed for computing
functions have been proved to be no more powerful than the lambda calculus, it captures the idea of computable functions as well as we
Introduction to λ Calculus is publicly available here and here.