Lambda Calculus Reducer

Out of boredom, I created a project that represents lambda calculus terms as list structures, and provides blocks for constructing, reducing and converting them to other forms.

As an example of what you can do, this is how you might use Snap! to construct the 'successor' function for Church numerals:

(Don't mind the control block =, that's just there so you can define variables within reporters. The new var block reports a new variable every time, which is why it's necessary here. You can still construct terms without it!)

Here is the resulting data structure, blockified for visibility:

Those numerical IDs are used to disambiguate between different variables with the same name.

You can convert lambda terms back into constructor blocks:

Calling the reported procedure reports back the original data structure.

You can convert terms into text:

You can convert them into working Snap! procedures, thanks to the new script-building capabilities of the join and split blocks:

This can be used to convert values into other Snap!-friendly forms, such as church numerals into Snap! numbers:

Oh, this is wonderful! Thank you so much for inventing it!

I've been trying to invent Church numerals this way:
but it doesn't work because I haven't yet convinced Jens to change the scope rules for upvars so that I can use the same name in two lambda expressions in the same toplevel script.

I'll have to see if I can preprocess my lambda expressions to use your idea of turning all the variable names into gensyms.

Edit: Uh oh, something in v7 has broken my project even worse, so I get no-such-variables errors. It worked better in v6, just getting wrong answers sometimes. I was confused.