Data types as graphical shapes

A very interesting idea that I've just found in a post by Aaron Spiegel: to explain basic FP constructs like map, filter and fold/reduce graphically (nothing new, I've already done that several times), but with an interesting twist: by representing types as shapes. That's a clever trick to better explain that HOFs (Higher-Order Functions).

However, visual languages rapidly become inadequate to express more high level concepts. For example you can sort-of encode algebraic data types using different colors for example. Then maybe you can express options using full or empty shapes. But, as you probably can see, there are limits in this medium and we can reach them pretty fast.

In some sense it's like understanding certain mathematical concepts using geometry (as a visual learner, that's how I really understood integrals), but one of the reasons mathematicians use textual notation is that it's much more concise and expressive.

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