[crabbone]

> If you can't create a value of type PrimeNumber that doesn't contain a prime number

Because you wrote a validation function, the exact thing OP told you not to do. Hooray?!

The goal of OP was to create a type that incorporates constraints on data, just like in their example about the non-empty list they created a type that in the type itself contains the constraints s.t. it's impossible to implement this type in a way that it will have an empty list.

You did the opposite. You created a type w/o any constraints whatsoever, and then added a validation function to it to make sure you only create values validated by that function. So... you kind of proved my point: it's nigh impossible to create a program intelligible to human beings that has a "prime number" type, and that's why we use validation -- it's easy to write, easy to understand.

Your type isn't even a natural number, let alone a prime number.

[chowells]

Are you aware that it's impossible to do any kind of parsing without validating the data? Saying "you have a validation function" is not some sort of disproof of parsing.

Parsing is an additional job on top of validation - providing type-level evidence that the data is good. That's what makes it valuable. It's not some theoretical difference in power. It's better software engineering.