On: An epic treatise on error models for systems programming languages

[looperhacks]

The "sum" and "product" is more about the cardinality of the type. If you have a type A with 3 possible values and B with 5 possible values, then the sum type X = A+B has 8 possible distinct values while the product type Y = A*B has 15 possible values

[marcosdumay → looperhacks]

Yeah, that's the bad definition that leads to problems like the one the OP describes.