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Re: Lambda calculus and it relation to LISP

From: Charles Matthews
Subject: Re: Lambda calculus and it relation to LISP
Date: Sat, 5 Oct 2002 08:58:57 +0100

"gnuist" wrote

> I read the following quote in a book on emacs and similar
> things in a book on lisp.
> "The lambda calculus is a mathematical formalism
> having to do with the way functions instantiate
> their arguments. To some extent it is the theoretical
> basis for Lisp and plenty of other computer languages."
> I am interested in a little concrete elaboration
> of this statement by any mathematicians, logicians
> or practitioners/users of lisp and lisp in emacs.

There are a few obstacles in understanding what is going on here.  For

- the lambda calculus may be a 'mathematical formalism', but it is not one
mathematicians usually have a feeling for, unless they have cause to use it
in some way: what it is really is a very basic piece of syntax for computer

- the underlying programming theory of lambda calculus is functional
programming, so on the whole it might be more accurate to call lambda
calculus a mechanism for expressing accurately the substitution of one
function in another, rather than instantiation (an operational rather than a
mathematical difference);

- you can call LISP a functional programming language if you want - not
everybody would so want;

- the untyped lambda calculus written in the usual compressed way
abbreviates heavily, and going a couple of steps back to a more tree-like
representation of combinators is much more perspicuous.

So, this connection can be made ... but joining it all up required a fair
amount of background.


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