[kazinator]

Lisp gives you a programming language in which you don't have to write a cryptic 42 page one-liner to have an implementation of lambda calculus.

Lisp gives you a way to talk about lambda calculus, in a way that executes. For instance, papers about lambda calculus may talk about "beta reduction" and things of that nature. Those concepts are not in lambda calculus; they are about lambda calculus.

In lambda calculus examples you have terms like \x x and whatnot. But lambda calculus doesn't explain what x is; x is an identifier and that is part of the description of lambda calculus, and not in lambda calculus.

Lisp has the batteries included for describing languages, such as lambda calculus. It has an answer for what is x: it's a symbol, available as a data type. It has an answer for what is "beta reduction"; it's a function you can write, and execute on some piece of lambda calculus.

Lisp closes the circle; the stuff you talk about in a paper can become code, and code which is not far from what the paper talks about.

[somewhereoutth]

Beta reduction is in fact the essence of LC - without it all you'd have is a nice tree.

The beauty and generality of LC is that x doesn't need an explanation, it is just a placeholder, yet that is enough to define interesting (perhaps all) things.

Lisp is an abstraction, that per article can be built upon the deeper abstraction of LC - question is, what does it give us in terms of expressiveness and understanding?

[tromp]

> Lisp gives you a programming language in which you don't have to write a cryptic 42 page one-liner to have an implementation of lambda calculus.

You totally misunderstood what the 42 pages are. They are not an implementation of LC, but an implementation of LISP in LC.

> Lisp gives you a way to talk about lambda calculus, in a way that executes.

LC gives you that too; it allows you to encode lambda terms as bitstrings, which can be represented as lambda terms themselves.

> But lambda calculus doesn't explain what x is

In the binary encoding, x is a de-Bruijn index: a natural number indicating the nesting level of the binding lambda.

> Lisp closes the circle

So does Binary Lambda Calculus.

[kazinator]

> You totally misunderstood what the 42 pages are.

There is a deliberate reversal of roles in my sentence that may not be obvious at a glance.