Where does the lambda come from?

[Twan Laan]

I'm wondering why a "lambda" in lambda calculus is used.
I heard some rumours that the notation \lambda x.f originates from
Russell's notation (he wrote \^x.f), that Church (in his 1932/1933
paper where he introduced lambda calculus) wanted to write ^x.f,
that some printer misinterpreted Church's intentions, and printed
\lambda x.f.

Does anybody know whether this rumour is true? If so, can you give
a reference to a paper or book where this is mentionned?

Any help is appreciated.

Twan Laan.
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[Jonathan P. Seldin]

In article <528gj9$p...@wsinfm06.win.tue.nl>, la...@wsinfm06.win.tue.nl
(Twan Laan) wrote:

Rosser, in "Highlights of the History of the Lambda-Calculus", Ann.
History of Computing vol. 6 no. 4 (Oct 1984) 337-349, says that this is
almost true. He says that the change from "^x.f" to the lambda notation
was made "for reasons of typography".

On the other hand, at the 1982 meeting of the conference on LISP and
functional programming, at which Church and Curry were honored by a
banquet at which both were present, I asked Church about this, and his
reply was that there was no particular reason for choosing lambda, that
some letter was needed and lambda happens to have been chosen.

So here are two of the principals whose memories differed by the early
1980s. There are several possibilities: Church simply did not remember
in 1982 how he had chosen the lambda notation, Rosser's memory played a
trick on him when he wrote his article, Church told this story to Rosser
[perhaps when Rosser was his graduate student], but intended the story to
be a joke, etc. Now that all of them are gone, I suspect the only way to
settle this would be to find some evidence (if ther is any) in the notes
Church left behind. Has anybody checked this?

I do think, however, that Church was using the lambda notation several
years before he sent his 1932/33 paper to the printer: I remember Curry
telling me that during his year at Goettingen (which was 1928-29), Church
was there for half the year, and Curry remembered that Church had a
manuscript in which there were many occurrences of the Greek letter
lambda. (Curry said that at the time he did not read enough of the
manuscript to see the connection with his own combinatory logic.)

--
Jonathan P. Seldin tel: 514-848-3254
Department of Mathematics sel...@alcor.concordia.ca
Concordia University, Montreal sel...@poincare.concordia.ca