I think there's one kind of "specification language" that works completely unlike programming itself—and that's the
interactive form of specification known as
requirements-gathering that occurs in the conversation between a contract programmer and their client.
I could see potential in a function-level spec in the form of an append-only transcript, where only one line can be added at a time. So you (with your requirements-specifier hat on) write a line of spec; and then you (as the programmer) write a function that only does what the spec says, in the stupidest way possible; and then you put on the other hat and add another line to the spec to constrain yourself from doing things so stupidly; and on and on. The same sort of granularity as happens when doing TDD by creating unit tests that fail; but these "tests" don't need to execute, human eyes just need to check the function against them.
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On another tangent: I've never seen anyone just "bite the bullet" on this, acknowledge that what they want is redundant effort, and explicitly design a programming language that forces you to program everything twice in two separate ways. It seems to me that it'd actually be a useful thing to have around, especially if it enforced two very different programming paradigms for the two formalisms—one functional and one procedural, say; or one dataflow-oriented ala APL or J, and the other actor-modelled ala Erlang.
Seems like something NASA would want to use for high-assurance systems, come to think of it. They get part-way there by making several teams write several isolated implementations of their high-assurance code—but it will likely end up having the same flaws in the same places, given that there's nothing forcing them to use separate abstractions.