Comment by sriku

This looks to me like partly a false dichotomy. We can design languages and write libraries. Some would even argue that some kinds of "libraries" could be viewed as languages themselves, as much as some languages might as well have been written as libraries in another language.

Also often, the language doesn't live isolated from its implementation (compiler or interpreter). While theory looks at languages via its semantics, in practice as the OP notes it is about the quality of the implementation and what can be reasonably done with the language.

A recent [1] case is Julia. I think it has hit a kind of sweet spot for language design where new performant code tends to get written in Julia rather than in some other language and bound to it. At its core, it is a simple "call functions, passing data in and getting results out" kind of language, but what the functions ("methods") mean and how the compiler does just-ahead-of-time compilation with deep type specialized code means you can write high level code that optimizes very well. Those mechanics operate under the hood though, which makes for a pleasant programming experience ... and there are loads of cutting edge packages being written in Julia. It is less interesting to look at Julia as "just the language".

[1] recent in programming languages is perhaps anything <= 15 years? .. because it takes time to discover a language's potential.