Alexis King, the author of the original "Parse, Don't Validate" article, also published a follow-up, "Names are not type safety" [0] clarifying that the "newtype" pattern (such as hiding a nonzero integer in a wrapper type) provide weaker guarantees than correctness by construction. Her original "Parse, Don't Validate" article also includes the following caveat:
> Use abstract datatypes to make validators “look like” parsers. Sometimes, making an illegal state truly unrepresentable is just plain impractical given the tools Haskell provides, such as ensuring an integer is in a particular range. In that case, use an abstract newtype with a smart constructor to “fake” a parser from a validator.
So, an abstract data type that protects its inner data is really a "validator" that tries to resemble a "parser" in cases where the type system itself cannot encode the invariant.
The article's second example, the non-empty vec, is a better example, because it encodes within the type system the invariant that one element must exist. The crux of Alexis King's article is that programs should be structured so that functions return data types designed to be correct by construction, akin to a parser transforming less-structured data into more-structured data.
[0] https://lexi-lambda.github.io/blog/2020/11/01/names-are-not-...