The title of this article, "Programming With Nothing", piques my interest.
I don't have a strong CS background, so this might be a silly question... But obviously, on a computer, "code" is really data, a series of bytes that instructs the processor what to do. In a literal sense, this sort of lamba calculus implementation isn't far removed from bog standard procedural programming. What's the actual philosophical background here-- what is a function, really? What makes it special?
Well, all sufficiently strong programming languages are equivalent in the Turing sense, and Turing machines are equivalent to lambda calculus in computational power.
That said, lambda calculus is rather different from standard procedural programming. The closest thing to it in the "real world" would be functional languages such as Scheme, ML and Haskell.
What makes functions special? I think the article answered that: with very simple ingredients, namely recursive functions that take only 1 argument, you can essentially write any program that you could write with full-fledged Ruby (or any other Turing-complete programming language).
Mathematically a function is a mapping from an input domain to an output domain. In the Lambda calculus a function is essentially a tuple of a variable name and a body lambda expression. Applying the function to an argument lambda expression gives you the body expression, where all ocurrences of the variable name are replaced with the argument expression. Essentially, the function can be understood as an replacement rule.
I don't have a strong CS background, so this might be a silly question... But obviously, on a computer, "code" is really data, a series of bytes that instructs the processor what to do. In a literal sense, this sort of lamba calculus implementation isn't far removed from bog standard procedural programming. What's the actual philosophical background here-- what is a function, really? What makes it special?