popeye VS olive-gui

Why not using Popeye instead of Fairy Stockfish? That way you can be sure about the stipulation.

I'm trying to came up with a suitable mathematical framework to study and detect themes in problems and, why not, choices made by players and engines in actual matches. I am somewhat inspired by the work by Guerino Mazzola in music composition, which mainly uses category theory to analize and compose music. I didn't study the inner workings of Popeye, so I might miss some fundamental knowledge.

Olive can be used to compose, test, and save your own compositions with, but not for playing through them.

The key is unique, as it should be! But as /u/Rocky-64 has already pointed out, there is a dual mate which is easily fixed by moving the player's king from e7 to f7. This is the sort of thing that a program such as Olive can help you spot.

In fact, the white king's only purpose is to have a white king on the board; it doesn't participate in the mate or try/set play at all. Likewise, the rook's only purpose is to wall off the f-file from the king. So (booting up Olive) the thought occurs to me that maybe we could put the king on e4 or e5 instead and do away with the rook altogether. This doesn't quite work, since we need to protect four squares on the f-file, but we can remedy that by putting the king on e4 and a second pawn on e5. Now we have a quieter key instead; 1.Kf4!, but at the cost of introducing the duals 1...Bf5 2.g4+/Kxf5. But we can remove the g- and h-pawns altogether, since they're not used in any other line! Now, it's a shame that Black still has the unprovided check 1...Bb7+, so maybe we put a pawn on b7 to stop that? In fact, looking again, it seems the only point of the pawn on e5 was to stop the check 2...Bc7+, so it might be better if we put a black pawn on c7 instead of a white pawn on e5, too...

Olive is a good tool for checking short problems (e.g. directmates, helpmates, selfmates, seriesmovers, fairy problems) for alternate solutions and the like.

This problem is badly cooked. Popeye (bundled with Olive) finds no less than nine different #3s.

I think it's definitely possible to be good at composing even if you're not that good at chess; especially if you use a tool such as Olive to validate your compositions, and if you actively look at what ideas are present in other people's compositions for inspiration. This is because, although it definitely helps to know some basic chess-playing tactical ideas, the ideas that come up in compositions are often very different from those that come up in real games. The previously-linked series of articles covers some key composition ideas in-depth.

Olive already has this in some capacity (the Auto Indexer).

Olive is a good tool for editing and testing your problem. Use it liberally. In particular, sometimes a try can be better than your original intended solution, in which case it may be worth making the try into the solution and the solution into a try.

Constructing a mate in two or three that avoids all the issues I've mentioned is actually not too hard with Olive to help catch cooks; making it thematic or longer is the real killer.

Also, download Olive! It's a GUI for Popeye, which is a problem-solving program that's especially good at move-limit stipulations. If you hit the "Defence 1" button, it'll even show you all the "almost-solutions", and sometimes these almost-solutions are worth changing your problem's theme for.