Chess invariants(muratbuffalo.blogspot.com) |
Chess invariants(muratbuffalo.blogspot.com) |
Nit: Pinning and the discovered check are not really rules, but rather names of tactics.
Rule 3.9.2: No piece can be moved that will either expose the king of the same colour to check or leave that king in check.
That's why treating colloquial concepts like "pinning" as though they are rules in and of themselves is not really precise or productive.
At the "Is this move legal?" level, they don't need unique rules of its own if the lower-level rules are specified correctly.
No piece can be moved that will leave the king of the same color in check.
Also, pinning can happen with pieces that don’t include a king, which means you can just move out of the pin and expose whatever other piece.
It’s just a chess tactic, not a rule. It’s like saying a chess skewer is a rule too.
As a kid playing chess with other neighborhood kids back in the day, absolutely none of us even knew about the en passant rule. My first exposure around the same time was completely by accident thanks to a passing reference in a CRPG called Betrayal at Krondor. It comes up in a story about a game that nearly costs an innkeeper her establishment when she loses because of a move she didn’t even know existed.
"Look, if this guys TLA+ logic struggles to model a 1,500-year-old game without crying over a French pawn-capture rule, you can't expect me to integrate Stripe billing without a few state invariant violations."
https://neuroning.com/boardgames-exercise/notebooks/walkthro...
The implementation makes it really easy to add new piece types or rules. For example, here's the full logic for rooks (sans castling):
(defn expand-pmove-for-rook [pmove]
(->> pmove
(expand-pmove-dirs [↑ ↓ ← →])
(pmoves-discard #(or (pmove-on-same-player-piece? %)
(pmove-changed-direction? %)))
(map pmoves-finish-capturing-opponent-piece)
(pmoves-finish-and-continue))))The post talks about "transition invariants" that should be somehow different from "state invariants" yet it describe them as:
> These are predicates over a <<state, next-state>> pair ...
i.e. it still is about state, but I find it much more useful to focus on behavior so instead of thinking about how state transition you focus on what the program is allowed to perform, regardless of the underlying data structure.
What I mean is that I'd like the code to tell me why a certain piece can't do such move instead of why it cannot transition it's position to another position and basically dumping its state in my head and there I have to execute the program myself.
The state transition is what the program is or isn't allowed to perform. The state they're talking about in the invariant isn't the program state, it's the game state.
As someone dabbling abit around chess engine development, I'm very often impressed by the many intricacies and observations made by people who pushed the envelope. It just doesn't sound plausible people wouldn't have discovered these killer invariants by now if they existed
Let's start from the other end. Just a pawn and two kings. It's possible to describe some quite succinct rules for when that's a draw versus a win for the side with the pawn. Agreed? Club players know these by heart. You could write that doen as invariants. As long as the side with the pawn stays inside the "green zone" of the state space, there is nothing the other side can do to void mate. And vice versa, if the game is in the red zone and the other player manages to stay inside that red zone, there is nothing the side with the pawn can do to win. Those areas of the state space, green and red zones, can be described as invariants, in contrast to just enumerating them. It's very compact and can easily be checked by a machine that it's correct.
Now let's add a pawn. And another. And a rook perhaps. The more you add, the harder the condition is to describe, but we live in the age of billion-node-sized neural nets, we have the resources. Eventually you get all pieces on the board, and if the starting position satisfies the draw invariant, that's it. And likely the 960 freestyle chess positions too.
There’s a book called Logic for Programmers: https://leanpub.com/logic#table-of-contents
While we're being pedantic though it's not a property of the piece that might be able to be moved that will place the king in check. It's a property of the move. For example we might imagine you have a rook between an enemy rook and your king. You can move the rook along the line between the enemy rook and the king, but not perpendicular to it.
The rule should be:
No move can be made where the moving players king is in check in the resulting position
I was pointing out that that specific rule (read to mean that moving a piece pinned against a king is not allow) is not strictly necessary. Putting oneself in check is not allowed regardless of whether it's because you moved a piece that was pinned against your king or moved your king directly into the line of sight of an opponent's piece. These are the different "means."
As a sibling comment points out, "The only action you can ever take in chess is moving," so it's not particularly meaningful to say that the only way to put yourself in check is by moving.
The rule, "3.9.2: no piece can be moved if that exposes or leaves its own king in check." covers both the case of moving a pinned piece as well as moving the king into check, i.e. it covers all "means" of putting yourself into check.