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From: "Charles Matthews" <charles.r.matthews@ntlworld.com>
Subject: Re: Lambda calculus and it relation to LISP
Date: Sat, 5 Oct 2002 08:58:57 +0100	[thread overview]
Message-ID: <UYwn9.92$gY1.17544@newsfep2-gui> (raw)
In-Reply-To: 9e8ebeb2.0210041920.2e480123@posting.google.com

"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

  parent reply	other threads:[~2002-10-05  7:58 UTC|newest]

Thread overview: 32+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2002-10-05  3:20 Lambda calculus and it relation to LISP gnuist
2002-10-05  7:51 ` Luke A. Olbrish
2002-10-05 10:46   ` William Elliot
2002-10-12  0:28     ` Alfred Einstead
2002-10-12  4:02       ` William Elliot
2002-10-05 11:44   ` David Kastrup
2002-10-09  4:38     ` James Wong
2002-10-09  4:48       ` William Elliot
2002-10-05  7:58 ` Charles Matthews [this message]
2002-10-05  8:05 ` Gareth McCaughan
2002-10-06 12:03   ` William Elliot
2002-10-06 19:22     ` Gareth McCaughan
2002-10-07  4:58       ` gnuist
2002-10-07  7:14         ` William Elliot
2002-10-07  7:37         ` Barb Knox
2002-10-07  9:34           ` David Kastrup
2002-10-07  9:59             ` William Elliot
2002-10-07 11:10               ` Barb Knox
2002-10-07 14:34                 ` William Elliot
2002-10-07 10:44             ` Christian Lemburg
2002-10-08  1:02               ` ozan s yigit
2002-10-07 10:59             ` Barb Knox
2002-10-08  3:05               ` David Kastrup
2002-10-07 23:12         ` Gareth McCaughan
2002-10-07  9:54       ` William Elliot
2002-10-07 22:48         ` Gareth McCaughan
2002-10-08  8:42           ` William Elliot
2002-10-05 14:46 ` Fred Gilham
2002-10-05 16:15 ` Kaz Kylheku
2002-10-06 12:22 ` Thaddeus L Olczyk
2002-10-06 13:46   ` Joona I Palaste
2002-10-12  0:36 ` Alfred Einstead

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