Agreed, it is unwieldy. However, because of it, eta-reduction is not as important because equivalent terms look the same, and name collisions can't happen. It made it a bit simpler.

And, that is definitely a bug, thanks. I think I could solve it by lazy evaluation (it wouldn't reduce that term) but I think I just need to correctly change vars when they move scope.

Not sure what you mean by "equivalent terms look the same". I'm not clear on how e.g. ##(2 1) and #1 look the same. Going by your remark about name collisions, I must ask if you are thinking of alpha-equivalence? (Which certainly is rendered unnecessary by the notational system.)

And thank you for making/hopefully fixing this!

Oh I see. Yes I was thinking of alpha-equivalence, sorry.

Now I must ask, do you know any good papers/algos on that reduction? And how would you envision animating? It seems a bit like a lambda/var pair just fall off...

I don't know what I might refer you to. Beta reduction requires recognizing subtrees of the form (#T S) (where T and S are any subtrees), eta reduction just requires recognizing subtrees of the form #(T 1) (where T is any subtree).

No idea about animation. It's really not something I'd thought about, I have to say...

Oops -- I forgot about the non-freeness requirement. So not just any subtree. That makes it trickier. But still not hard, I think.