Path: utzoo!news-server.csri.toronto.edu!rutgers!usc!wuarchive!uunet!mcsun!ukc!icdoc!syma!aarons
From: aarons@syma.sussex.ac.uk (Aaron Sloman)
Newsgroups: comp.lang.functional
Subject: Re: origin of lambda symbol
Summary: Frege first invented this kind of notation
Keywords: lambda, Church, lambda calculus, notation, Frege
Message-ID: <4700@syma.sussex.ac.uk>
Date: 10 Mar 91 23:57:45 GMT
References: <1991Feb27.165322.25377@cs.utk.edu>
Distribution: comp.lang.functional
Organization: School of Cognitive & Computing Sciences, Sussex Univ. UK
Lines: 43

mclennan@cs.utk.edu (Bruce MacLennan) writes:

> Date: 27 Feb 91 16:53:22 GMT
> Followup-To: why lambda ? (Daniel de Rauglaudre)
 ..........
> At the 1982 LISP and Functional Programming Conference I asked
> Alonzo Church about the origin of the lambda symbol.
 ..........
> Church said that the starting point was Russell and Whitehead's
> abstraction operator (in Principia Mathematica), which they wrote
> with a caret over the bound variable:  $\hat{x}(x^2+1)$.
 ..........

It is perhaps worth noting that the first person (as far as I know)
to use an operator that binds a variable as an abstraction operator
was Gottlob Frege, who also invented the existential and universal
quantifiers, though he used a cumbersome 2-D notation for
implication.

Russell learnt about Frege's notation as a result of reviewing his
work (I think it was the first volume of Frege's "The basic laws
(Grundgezetse) of arithmetic" the first full blown attempt to show

(a) that all concepts of arithmetic can be defined solely in terms
of purely logical concepts

(b) that all truths of arithmetic could be proved solely on the
basis of truths of logic.

Although Russell found that Frege's system was inconsistent (because
it allowed the formulation of Russell's paradox, concerning the set
of all sets that are not members of themselves), he continued to use
many of the ideas, though using a rather different notation.

I believe computer science owes a great deal to Frege's pioneering
work, including the generalisation of the notion of a function to
include predicates and higher order functions, and the first proper
analysis of variables.

Aaron Sloman,
School of Cognitive and Computing Sciences,
Univ of Sussex, Brighton, BN1 9QH, England
    EMAIL   aarons@cogs.sussex.ac.uk