Garth Wallace wrote on Thu, Nov 22, 2018 07:54 AM UTC:
Considering a move to be a set of changes on the board is, in fact, exactly where I ended up going with this. And you're right, it doesn't lend itself to a very compact notation—perhaps a summation-like notation could be introduced to make it easier to describe the common case where a subset of a pieces moves have a direct, progressive relation to each other (like riders). Though as an abstract formulation, it's really powerful. For example, castling is now easy to define. In fact, it seems like you can define nearly everything in the game in these terms, even things that aren't usually considered pieces or qualities of pieces.
I approached move induction in terms of Mimes. When I was still working with sequence-of-step paths, I basically gave up on describing them, which rankled because it meant that I couldn't use set operations like union or intersection on them like I could with "regular" pieces without a lot of hand-waving. When the analysis treats their behavior as "then a miracle occurs", you can't get very useful results. Knight-Relay would be the sort of thing that I wasn't able to deal with, since in that the pieces should really be describable as unions of regular pieces with very limited (knight-only) mimes, and I couldn't figure out how to describe a piece with moves that "changed".
After moving away from sequences, though, I realized that you could include the path from the "move-lending" piece to the mimic as part of the condition. This is basically equivalent to your first method, moving the mime onto the lender and back before proceding to its destination, except that there is no actual "moving", just checking to see if the right squares are unoccupied or occupied by the right pieces. This is nice because it means that mimes are still just sets of moves. The downside is that you can't really define a "generic" mime, since you have to know which pieces it can interact with. But in a way that makes sense, since you can't really draw any conclusions about what a mime is capable of without knowing what moves it can borrow anyway.
Similar reasoning can be applied to define Annan Chess (borrowing a move if there is an unbroken line backwards to the lender), and the Ultima Coordinator (actually simpler, since only the relative position of the friendly King matters).
Soon after hitting on this I realized that you could even apply this to the King's inability to move into check, by including tests for enemy attacks in all of the King's moves. Previously I'd assumed that royal status had to be dealt with in some way outside of this system, but it doesn't have to be. Royal status is really a blanket term that covers a few different qualities. It turns out that the rule against exposing a royal to check can also be expressed in this system, though counterintuitively it is a property of every other piece besides the royal.
Considering a move to be a set of changes on the board is, in fact, exactly where I ended up going with this. And you're right, it doesn't lend itself to a very compact notation—perhaps a summation-like notation could be introduced to make it easier to describe the common case where a subset of a pieces moves have a direct, progressive relation to each other (like riders). Though as an abstract formulation, it's really powerful. For example, castling is now easy to define. In fact, it seems like you can define nearly everything in the game in these terms, even things that aren't usually considered pieces or qualities of pieces.
I approached move induction in terms of Mimes. When I was still working with sequence-of-step paths, I basically gave up on describing them, which rankled because it meant that I couldn't use set operations like union or intersection on them like I could with "regular" pieces without a lot of hand-waving. When the analysis treats their behavior as "then a miracle occurs", you can't get very useful results. Knight-Relay would be the sort of thing that I wasn't able to deal with, since in that the pieces should really be describable as unions of regular pieces with very limited (knight-only) mimes, and I couldn't figure out how to describe a piece with moves that "changed".
After moving away from sequences, though, I realized that you could include the path from the "move-lending" piece to the mimic as part of the condition. This is basically equivalent to your first method, moving the mime onto the lender and back before proceding to its destination, except that there is no actual "moving", just checking to see if the right squares are unoccupied or occupied by the right pieces. This is nice because it means that mimes are still just sets of moves. The downside is that you can't really define a "generic" mime, since you have to know which pieces it can interact with. But in a way that makes sense, since you can't really draw any conclusions about what a mime is capable of without knowing what moves it can borrow anyway.
Similar reasoning can be applied to define Annan Chess (borrowing a move if there is an unbroken line backwards to the lender), and the Ultima Coordinator (actually simpler, since only the relative position of the friendly King matters).
Soon after hitting on this I realized that you could even apply this to the King's inability to move into check, by including tests for enemy attacks in all of the King's moves. Previously I'd assumed that royal status had to be dealt with in some way outside of this system, but it doesn't have to be. Royal status is really a blanket term that covers a few different qualities. It turns out that the rule against exposing a royal to check can also be expressed in this system, though counterintuitively it is a property of every other piece besides the royal.