No no, not your wife/partner/girlfriend, you can't program those, they have minds of their own. Actually this is not even my joke, it's in the GALasm documentation, see further down.
The GAL used is a 16V8 which is way way obsolete but still readily obtainable for a dollar or two. Here's an old tutorial on how to use them. Really I don't know why people don't use them more to replace a whole bunch of TTL or CMOS logic. For one thing if you make a logic error you only need to fix the equations and reprogram, not rework a whole bunch of ICs and connects. For more complicated logic there are CPLDs and FPGAs which are used by many projects on Hackaday.
One thing though, to program these GALs you need a hardware programmer. The popular TL866 programmer, besides doing (E)EPROMs, and many MCUs, also handles the 16V8.
A compiler takes logic equations and generates JEDEC files which are written into the GAL. You don't need a compiler if the project supplies precompiled JEDEC files. But I wanted to learn to use such a tool for future reference. The compiler I used is the open source GALasm at Github. I found and fixed some issues with the code that provoked warnings from recent gcc versions and submitted a pull request, which the current maintainer gracefully accepted.
I have successfully programmed and verified a GAL. So that's the second goal accomplished. But bear in mind, I have not soldered a single joint or powered up anything yet. The true test is yet to come.