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I assume you can simulate a turning machine with it.

I don't know about turning machines, but it can certainly simulate Turing machines. You can even interpret Brainfuck, a Turing Machine inspired esoteric language, in under 104 bytes [1].

[1] https://tromp.github.io/cl/Binary_lambda_calculus.html#Brain...

It’s a beautiful reification of de Bruijn indices. Thanks!

I’m kind of tempted by the idea of sugaring it using symbol properties such that one could use obfuscating names without breaking the elegant alpha compare and convert.

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