> A formal specification language is a programming language that we don't know how to compile.

Not really, on both counts.

Firstly they're not really programming languages in the usual sense, in that they don't describe the sequence of instructions that the computer must follow. Functional programming languages are considered 'declarative', but they're still explicit about the computational work to be done. A formal spec doesn't do this, it just expresses the intended constraints on the correspondence between input and output (very roughly speaking).

Secondly, regarding the we don't know how to compile it aspect: 'constraint programming' and SMT solvers essentially do this, although they're not a practical way to build most software.