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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
example:
- 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
science;
- 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.
Charles
- Lambda calculus and it relation to LISP, gnuist, 2002/10/04
- Re: Lambda calculus and it relation to LISP, Luke A. Olbrish, 2002/10/05
- Re: Lambda calculus and it relation to LISP,
Charles Matthews <=
- Re: Lambda calculus and it relation to LISP, Gareth McCaughan, 2002/10/05
- Re: Lambda calculus and it relation to LISP, William Elliot, 2002/10/06
- Re: Lambda calculus and it relation to LISP, Gareth McCaughan, 2002/10/06
- Re: Lambda calculus and it relation to LISP, gnuist, 2002/10/07
- Re: Lambda calculus and it relation to LISP, William Elliot, 2002/10/07
- Re: Lambda calculus and it relation to LISP, Barb Knox, 2002/10/07
- Re: Lambda calculus and it relation to LISP, David Kastrup, 2002/10/07
- Re: Lambda calculus and it relation to LISP, William Elliot, 2002/10/07
- Re: Lambda calculus and it relation to LISP, Barb Knox, 2002/10/07
- Re: Lambda calculus and it relation to LISP, William Elliot, 2002/10/07