Some more numbers as lambda calculus

On Reddit, u/spriteguard asks:

Do you have any diagrams of smaller numbers for comparison? I’d love to see a whole sequence of these.

I have work to put off, so I couldn’t resist the challenge. Like the previous post, these are Tromp diagrams showing lambda calculus expressions that evaluate to Church integers.

Multiplication: λa b f. a (b f)
10 (represented as 2 × 5)
100 = (2 × 5)^2
A googol
A googolplex
A googolduplex
Decker (10↑↑↑2)
Graham’s number
My own large number, f_{ω^ω + 1}(4) in a version of the fast-growing hierarchy where f_0(n) = n^n
A truly huge number, f_{Γ_ω + 1}(3)

Code to generate these diagrams is on Github; I generated these with the command

./trylambda --outdir /tmp/out demofiles/smallernums.olc demofiles/graham.olc demofiles/fgh.olc demofiles/slow.olc

Published by Paul Crowley

I'm Paul Crowley aka "ciphergoth", a cryptographer and programmer living in Mountain View, California. See also my Twitter feed, my webpages, my blogs on Dreamwidth and Livejournal, and my previous proper blog. Or mail me: paul at

3 thoughts on “Some more numbers as lambda calculus

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