Property-based testing for a chess game

I'm trying to wrap my mind around property-based testing and chess. Currently I represent my chess game as a 2d-array and the only pieces I have implemented are pawns and knights for grokking this.

The pawn and knight represent their moves as the set of allMoves(x,y) \ invalidMoves(board,x,y). So one property I can think of is to test that allMoves(x,y) ∪ invalidMoves(board,x,y) === allMoves. But beyond that I'm not sure what else to test. I assume that I need to set up a simplified oracle model for the chess board but I'm not sure what such a model would be.

Solution

Start by just saying some obvious things that are true about real-life chess boards, no matter how dumb they sound. Many of those will be reasonable properties to test. Here are some ideas:

When you move a piece, it moves from the place where it was to the place where the move puts it.
No legal knight move is ever a legal pawn move.
A pawn never moves more than two squares at once.
A knight never moves adjacent to its starting position.
A move should only involve positions actually on the board.
Moving onto another piece decreases the number of pieces on the board.

Many more ideas like this exist. They seem simple, but I guarantee your early implementations will miss some of them. Figure out how to write these invariants as properties, and grow your test suite from there.