[kazinator]

Lisp does not come from lambda calculus. Anonymous functions in Lisp get their LAMBDA name from lambda calculus, that's all. MacCarthy admitted that he didn't even understand lambda calculus properly, which is why early Lisp was dynamically scoped: lambdas didn't capture lexical variables. Whereas lambda calculus is lexical. Lexical scoping was adopted in later Lisp dialects and into Common Lisp, making those dialects retroactively related to lambda calculus. (Emacs Lisp shows the traditional behavior of dynamic scoping; therefore it couldn't be said to be related to lambda calculus.)

Lambda calculus is a formalization of number theory which builds up numbers from functions. An important result is that lambda calculus is Turing complete. It shows that we can boostrap numbers and number theory from almost out of nothing, using Church numerals.

Lisp has never built numbers out of Church numerals; it had ordinary integers.

Also, lambda calculus, typed or not, does not have its own syntax as a data type. It doesn't have symbols. You don't quote a symbol and pass it to a function and so on.

So that's basically it; there is a link between Lisp and lambda calculus due to the use of the word lambda in a related way, and a somewhat stronger link between lexically scoped Lisps (which came later) and lambda calculus.

[js8]

I guess you're right, it doesn't come so much from lambda calculus as I claimed, it was more inspired by it. Although to be fair, in the time the Lisp appeared, it was the closest thing (by a wide margin) to lambda calculus. I think it was a valiant effort to bridge the gap in that direction (and the design choices were influenced by the trade off that he also wanted a practical programming language).

Also, even languages like Haskell are not based only on theoretical lambda calculus, but they also have primitives for data types, which could be, in theory, represented by lambda expressions.