What does the "Lambda" in "Lambda calculus" stand for?



I've been reading about Lambda calculus recently but strangely I can't find an explanation for why it is called "Lambda" or where the expression comes from.

Can anyone explain the origins of the term?


Posted 2016-04-13T12:58:53.817

Reputation: 585



An excerpt from History of Lambda-calculus and Combinatory Logic by F. Cardone and J.R. Hindley(2006):

By the way, why did Church choose the notation “$\lambda$”? In [Church, 1964, §2] he stated clearly that it came from the notation “$\hat{x}$” used for class-abstraction by Whitehead and Russell, by first modifying “$\hat{x}$” to “$\wedge x$” to distinguish function abstraction from class-abstraction, and then changing “$\wedge$” to “$\lambda$” for ease of printing. This origin was also reported in [Rosser, 1984, p.338]. On the other hand, in his later years Church told two enquirers that the choice was more accidental: a symbol was needed and “$\lambda$” just happened to be chosen.

Anton Trunov

Posted 2016-04-13T12:58:53.817

Reputation: 3 179

4And lambda is the name of the greek letter “λ” chosen as the symbol. – Thorbjørn Ravn Andersen – 2016-04-16T11:33:12.013


here is some other near-firsthand info/ angle on this by Church student Dana Scott as just reported by Ghica and documented in a youtube video.[1]

He says that when Church was asked what the meaning of the λ was, he just replied “Eeny, meeny, miny, moe.“, which can only mean one thing. It was a random, meaningless choice. Prof. Scott claimed that the typographical origin myth was mainly propagated by Henk Barendregt and is just pure whimsy. He asked us to stop perpetrating this silly story.

[1] Dana Scott on lambda notation / youtube

[2] why is lambda calculus named that / math.SE


Posted 2016-04-13T12:58:53.817

Reputation: 9 131