λ²

λ² is a λ-calculus implementation written only in Python lambdas.

• No recursion.
• No Python built-ins (integers, strings, conditionals... nothing!).
• No external dependencies. (Duh.)

What is this?

From the Wikipedia entry on λ-calculus:

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any single-taped Turing machine and was first introduced by mathematician Alonzo Church in the 1930s as part of his research of the foundations of mathematics.

Binary λ-calculus is just a convenient encoding for already valid λ-calculus programs. 00 is abstraction and 01 is application. Instead of variables, binary λ-calculus uses De Bruijn indexes.

Why?

Why not?