Why is lambda calculus named after that specific Greek letter? Do not believe the rumours!

A common myth in theoretical computer science is that the ‘λ’ in λ-calculus comes from some kind of typographical error, where the intended notation was a circumflex accent ŷ.M, which became a caret ^y.M then finally a lambda λy.M. At least on the math stack-exchange this is the most popular explanation [link].

We recently had λ-calculus pioneer Prof. Dana Scott give a series of lectures in our School. He was a PhD student of Alonzo Church. In the introduction of one of his lectures he told us the story of the Greek letters used in the λ-calculus: the α of α-conversion, the β of β-expansion, the η of η-expansion and of course λ itself.

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.

I am attaching the link to the YouTube video with apologies for the low quality.

About Dan Ghica

Reader in Semantics of Programming Languages // University of Birmingham // https://twitter.com/danghica // https://www.facebook.com/dan.ghica
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