What type of lambda calculus would Lisp loosely be an example of?

Question

I\'m trying to get a better grip on how types come into play in lambda calculus. Admittedly, a lot of the type theory stuff is over my head. Lisp is a dynamically typed la

Answer 1

John McCarthy introduced LISP in his April, 1960 paper "Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I". The following paragraph is from page 6:

e. Functions and Forms. It is usual in mathematics — outside of mathematical logic — to use the word “function” imprecisely and to apply it to forms such as y² + x. Because we shall later compute with expressions for functions, we need a distinction between functions and forms and a notation for express- ing this distinction. This distinction and a notation for describing it, from which we deviate trivially, is given by Church [3].
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3. A. CHURCH, The Calculi of Lambda-Conversion (Princeton University Press, Princeton, N. J., 1941).

The Wikipedia article on lambda-calculus has a history of Church's publications. The 1941 paper referenced by McCarthy seems to be about the typed lambda-calculus, in contradiction to the Wikipedia article's introduction.

The lambda keyword in Lisp can be understood to refer to the lambda-calculus only through analogy. A Lisp lambda expression is a type of anonymous function.