Newsgroups: comp.lang.lisp
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From: hbaker@netcom.com (Henry G. Baker)
Subject: Re: [history question] Why was typed lambda calculus not used?
Message-ID: <hbakerCyww5K.F62@netcom.com>
Organization: nil
References: <PP000547.94Nov5004912@bedlam.interramp.com>
Date: Mon, 7 Nov 1994 19:15:20 GMT
Lines: 38

In article <PP000547.94Nov5004912@bedlam.interramp.com> bhogan@rahul.net (Bill Hogan) writes:
>
>  Church's typed lambda calculus, published in 1940, seems to be at
>least as interesting as his type-free lambda calculus published four
>years earlier, yet the various implementations of Lisp that I find
>today seem to be based exclusively on Church's type-free lambda
>calculus.
>
>  Is this merely because versions of Lisp that are based on Church's
>typed lambda calculus exist but I am not aware of the fact, or is it
>because the first developers of Lisp debated the question and decided
>to base Lisp on Church's type-free lambda calculus instead of basing
>it on his typed lambda calculus?

McCarthy freely admits that he didn't really understand _any_ lambda
calculus when he invented the first Lisp.  If he _had_ understood,
then it would have had static variable scoping, and probably lazy
evaluation, as well.  I seem to recall that he briefly glanced at
Curry & Feys, but didn't understand the alpha-renaming rule (the one
that does static variable scoping).

On the other hand, Lisp had 'eval' and cons cells, which the lambda
calculus didn't have.

So it is probable that he wasn't aware of the typed lambda calculus at
the time.

Michael Levin is one of the early Lisp people who had a mathematical
logic bent, and he prepared some course notes at MIT which I found
absolutely fascinating.  I highly recommend getting MIT/LCS/TR-131,
'Mathematical Logic for Computer Scientists', Michael Levin, June
1974, approx. 175 pages.  It proves undecidability by means of Lisp
eval.

      Henry Baker
      Read ftp.netcom.com:/pub/hbaker/README for info on ftp-able papers.
      Contact hoodr@netcom.com if you have trouble ftping

