Re: [HM] lambda functions

Michael S. Mahoney (mike@Princeton.edu)
Mon, 09 Aug 1999 17:43:22 -0400

Scheme took lambda from Lisp, whose creator, John McCarthy, took it from
Alonzo Church's lambda calculus. According to Church's student, J.
Barkley Rosser ("Highlights of the History of the Lambda-Calculus",
Annals of the History of Computing 6,4 [1984], 337-349; at 338), Church
took the notation from Whitehead and Russell's Principia Mathematica,
where the class of all x such that f(x) was written as xf(x) with a caret
(^) over the first x. Rosser continues: "Because the new concept
differed quite appreciably from class membership, Church moved the caret
from over the x down to the line just the left of the x; specifically
^xf(x). Later for reasons of typography, an appendage was added to the
caret to product a lambda; the result was <lambda>xf(x)." (The original
has, of course, the Greek letter where I have written <lambda>.)

For the early history of the lambda calculus, see Rosser's article and
that of his fellow graduate student, Stephen C. Kleene, "Origins of
Recursive Function Theory", in Annals of the History of Computing
3,1(1981), 52-67.

msm

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Michael S. Mahoney Department of History Princeton University
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