A computational language is designed to help us think computationally
Stephen Wolfram defines a computational language as different from a general purpose programming language. Computational languages, like Mathematica, are designed to help us think computationally.
Programming languages, on the other hand, are designed for efficient instruction to the computer, telling it exactly what to do.
It intuitively makes sense that there should be a divide between Productions Systems and using computational language as a Medium for thinking. Stephen Wolfram uses the analogy of mathematical notation - once notation was invented, it opened the way to the invention of the mathematical natural sciences. But how precisely should a computational language differ?
We sometimes classify languages in terms of "higher-level" versus "lower-level" languages, but that high versus low isn't specific enough. Rather, we should tailor the language to have the appropriate conceptual constructs for the domain in which it's being used.
So what is a computational language? It’s a language for expressing things in a computational way—and for capturing computational ways of thinking about things. It’s not just a language for telling computers what to do. It’s a language that both computers and humans can use to represent computational ways of thinking about things. It’s a language that puts into concrete form a computational view of everything. It’s a language that lets one use the computational paradigm as a framework for formulating and organizing one’s thoughts.