I am developing my own programming language, but I have no specification written for it. When people tell me that I need a specification, I reply that I already have one - the source code of the language compiler.
I feel like if you’re designing a language, the activity of producing the spec, which involves the grammar etc., would allow you to design unencumbered by whether your design is easy to implement. Or whether it’s a good fit for the language you are implementing the compiler with.
The OP also correctly identifies that thoughtful design takes a back seat in favor of action when we start writing the code.
So unless you want bugs to be your specification, you actually need to specify what you want.
If you want a specification from source code, you need to reverse engineer it. Although that’s a bit easier now, with LLMs.
Pure specification itself is useless without actual implementation (which does the job), so, trying to write such specification (in a natural language) has no practical sense.
A specification describes the externally observable behavior, constraints, and properties of a system. That's independent of how those properties are implemented.
An implementation is a concrete realization of a specification, that achieves the specified behavior using particular algorithms, data structures, and operational mechanisms.
> Pure specification itself is useless without actual implementation (which does the job), so, trying to write such specification (in a natural language) has no practical sense.
That's a non sequitur, i.e. the part of your sentence after the commas doesn't follow from the first part.
"Pure specification itself" has a purpose, which is to guide implementations. That's the "practical sense".