This is really thin and needs more work but at least I was able to get the Observable notebook to call a program in Wolfram Cloud and actually obtain a JSON output of a symbolic computation e.g. Fourier Transform.
But that’s not all, the Mathematica Notebook is not simply called with some functions in it, instead the interface to the Mathematica Notebook is a Free Form mix-mode math expressions and English!
Example: FourierTransform Sin(x times 2)
The latter computes the same as Sin(x^2)
When the Observable porgrammer makes the API call to the Mathematica Notebook he or she need not be a Mathematica programmer and learn the horiffic crap of how to call its functions and worse how to format the output back into the Observable notebook!
Rather the programmer enters free form mixed-mode text to access the Mathematica Notebook in the Wolfram Cloud and results are returned in JSON.
This exmpowers the Observable developers to have the good of both worlds without sacrificing their sanity and learn Mathematica.
You must have head of Wolfram Alpha, well this is a mini-customized Wolfram Alpha (not really it is our home brewed code) which uses PLI to build the Free Form grammar:
Programmable Linguistic Interface
But wait! We are not limited to just Free Form Mathematical expressions we can have physics free form , chemistry, biology and genome and much more
JSON output is primitive I need to call techsupport @ wolfram to improve it.