It's extremely formalized, but at least for me the foundation I always come back to to try to explain type systems is the taxonomy in chapter 1 of Stepanov and

It's extremely formalized, but at least for me the foundation I always come back to to try to explain type systems is the taxonomy in chapter 1 of Stepanov and McJones's Elements of Programming[0]. Type systems help ensure your binary data are well-formed value (and your bits are numbers, your numbers are temperatures, etc. up various hierarchies). I find this is more convincing initially for mechanically sympathetic programmers (including myself) than any taxonomy of endofunctors. [0] http://elementsofprogramming.com/ http://elementsofprogramming.com/