[fnordian_slip]

Apologies for posting a completely off-topic comment, but as an ESL person this interests me.

I would have thought that both were different, but grammatically correct, with almost identical meaning.

"A properly written sentence" is a sentence that is properly written, and "a proper written sentence" is a written sentence that is proper.

But now I have achieved semantic saturation, and am not sure anymore.

[BossingAround]

From [1], "Adjectives modify nouns; adverbs modify verbs, ..." - so though you're right that both sentences are grammatical, I think a lot of styles would have a problem with "a proper written sentence" since what you actually mean to say is "a properly written sentence" (unless you make it clear that you speak of "proper sentences", probably).

[1] https://owl.purdue.edu/owl/general_writing/grammar/how_to_us...

[gilleain]

Perhaps.

The way I read it, the choice of "proper written sentence" gives it the flavour of "Proper. Written. Sentence" - as in, with an annoyed emphasis.

As always, you can apply rules to English if you like, but sometimes they are optional.