Chess Invariants

(muratbuffalo.blogspot.com)

49 points | by ingve 4 hours ago ago

31 comments

  • vunderba 24 minutes ago

    > Chess is a lot trickier than it looks. It has so many rules: castling, en passant, pawn promotion, pinning, the discovered check, and the deadlock case of stalemate.

    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.

  • yewenjie 3 hours ago

    > Chess is a lot trickier than it looks. It has so many rules: castling, en passant, pawn promotion, pinning, the discovered check, and the deadlock case of stalemate.

    Nit: Pinning and the discovered check are not really rules, but rather names of tactics.

    • JohnKemeny 3 hours ago

      Well, if a piece is pinned it's illegal to move it.

      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.

      • TheOtherHobbes 3 hours ago

        Unlike en-passant and castling, pinning and discovered checks are consequences of lower-level rules.

        At the "Is this move legal?" level, they don't need unique rules of its own if the lower-level rules are specified correctly.

        • JohnKemeny 3 hours ago

          3.9.2: no piece can be moved if that exposes or leaves its own king in check.

          • 333c 3 hours ago

            That's a consequence of not being allowed to put yourself in check (by any means).

            • anamexis an hour ago

              The only way to put yourself in check is by moving.

              • yifanl an hour ago

                The only action you can ever take in chess is moving.

              • 333c an hour ago

                Did you mean putting your opponent in check? In chess, you are not allowed to put yourself in check.

                • anamexis 36 minutes ago

                  You said “ That's a consequence of not being allowed to put yourself in check (by any means).” My point is that there are no other means.

                  • 333c 7 minutes ago

                    I was replying to a comment quoting an official rule saying "no piece can be moved if that exposes or leaves its own king in check."

                    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.

      • gobdovan 3 hours ago

        You can also pin a pawn to a queen, but the pawn can still legally move.

        • HiroProtagonist 2 hours ago

          You're both right, depending on whether you mean relative pin vs absolute pin.

      • munchler 3 hours ago

        The point is that, logically, the first part of that rule (“expose the king”) is implied by the second part (“leave that king”), so the first part is redundant. You could simplify the rule to:

        No piece can be moved that will leave the king of the same color in check.

        • emil-lp 2 hours ago

          You should submit it to FIDE.

      • saberience an hour ago

        Pinning isn’t a rule, it’s just something that arises from other rules.

        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.

    • juujian 3 hours ago

      And discovered check means that it is not sufficient to check the position of the piece you have moved, you also need to check the position of other pieces to see whether there is a new check.

  • NicoHartmann 3 hours ago

    I can't wait to show this to my manager next time he asks why it's taking three weeks to build a simple CRUD app.

    "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."

    • epolanski 2 hours ago

      Payments have a gargantuan amount of possible transitions and invariants that are far from trivial to encode.

  • ferd 2 hours ago

    Shameless plug: a code walkthru modeling the rules of chess, ment as an exercise/teaching functional programming (in Clojure):

    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))))
  • duesabati 2 hours ago

    While I think everything written in this post is correct, what really is starting bothering me is this over-focus/attention on data even when what you want to express is behavior, let me explain:

    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.

  • nilslindemann 33 minutes ago

    I read these images of source code the same way as I read images of math formulas on Wikipedia: Not at all.

  • rauljara 2 hours ago

    Anyone know what language is being used in the blogpost?

  • unprovable 4 hours ago

    If you like this, you're probably gonna like this: https://en.wikipedia.org/wiki/Chessboard_complex

    • srean 2 hours ago

      This is delightful. Thanks.

  • vintermann 2 hours ago

    That king promotion rule sounds like it made the game more fun.

  • efavdb 2 hours ago

    One king per color?

  • phoe-krk 2 hours ago

    Screenshots of code? In 2026?...

  • fnord77 2 hours ago

    side question, which CS class(es) teach about invariants?