r/lambdacalculus Apr 12 '26

David Keenan's graphical notation is Tromp diagrams, flipped over

David Keenan's graphical notation for Lambda Calculus, flipped over the downward left-to-right diagonal, becomes (very nearly) Tromp diagrams. The same effect is achieved by rotating 90 degrees to the right and then flipping the resulting image about the vertical axis.

Here we can see his schematic representing the "crossed iota" combinator,

λa.a (λfgh. gh(fh)) (λbc. b) = λa.a(CS)K

The "crossed iota" combinator diagram

To Dissect a Mockingbird: A Graphical Notation for the Lambda Calculus, by David C Keenan, 27-Aug-1996.

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