Chess Invariants

8 hours ago

Chess is a complex concurrent system with interleaved execution and numerous rules.
Invariants in chess are split into state invariants (predicates over a single state) and transition invariants (predicates over a step).
Key state invariants include TypeOK, OneKingPerColor, BothKingsOnBoard, TurnParity (linking move count to player turns), PreviousPlayerNotInCheck, and NotBothInCheck.
Transition invariants like MoveCountStrictlyIncreases, TurnAlternates, PieceCountNonIncreasing, SingleCapturePerMove, and ExactlyTwoSquaresChange describe constraints on state changes.
Basic invariants may be violated when adding rules like castling (breaks ExactlyTwoSquaresChange) or en passant, while others like PieceCountNonIncreasing survive pawn promotion.

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