Uhm, if it's "web-hosting", chances are you only have "web" space. I.E. you can place pages, and probably jsps, servlets, phps, asps, etc there, as well as at least a small "download" area, but anything else is a system application and those lie outside the realm of "web-hosting". Ask your provider about any possible "equivalent" services that they may (and probably do) already provide (which also includes DB services, of course), or are willing to install and make available.
Now, as stated above, if you have a "dedicated" server, virtual or not, then do what you wish, that is much more than simple "web-hosting", so I can only assume that this is not what you have.
APLX is a very complete implementation of the APL programming language from MicroAPL. The company stopped producing it in 2016 and it has been taken over by Dyalog. While Dyalog ...