Set filtersSome filters are special in that they represent a set of squares in the current position. That is, applied to a particular position, one of these filters is associated with a set of squares. (Sometimes we write just "set" for "set of squares" or "square set". Sometimes we say the filter "returns" the set of squares.
Filters that are associated with square sets are called "set filters".
The most common kind of set filter is the piece designator. A piece designator, like
.f1-3 represents the set of squares in the current position that are occupied by the piece types it denotes on the squares it denotes.
For example, suppose the current position is the starting position of chess. Then the piece designator R is associated with the set of squares a1 and h1. The piece designator
[Rr] is associated with the set of squares
[Nn]h1-8 is the set of squares that have a knight on them on the h file, namely
The piece designator
_d1-8 is the empty squares on the d file, namely
d6. The piece designator
[Q_]d1-8 would add to that set the square
Not all filters are set filters. For example,
relation are not set filters. The set filters are described in the following table:
|name of set filter||associated set|
|attack||the set of squares in its second argument attacked by a piece on a square in its first argument|
|.||all squares on the board|
|move||the set of destination squares of any matching move|
|lightsquares||the set of light squares|
|darksquares||the set of dark squares|
|piece||the set of squares to which the associated piece variable is bound making the subsequent filters true|
|square||the set of squares to which the associated square variable is bound making the subsequent filters true|
|ray||the set of squares terminating a ray described by the |
|direction filters||the squares that are the specified distance, in the specified directions, away from its argument|
|not||if its argument is a set filter, then all squares not in the squares denoted by that argument|
|on||the intersection of the sets denoted by its arguments|
|or||if both its arguments are sets, then the union of the sets denoted by those arguments|
|_||the empty squares|
|piece designators||the squares described by the piece designator|
The documentation for the filter will describe more precisely the set the filter is associated with. The filter "move" for example, is the set of destination squares of any move that occurs from the current position. If White's first move was 1.e4, then if the current position is the initial position,
move from . is the set e4.
The significance of this is that many filters have arguments that are sets. For example, the
attack filter is associated with the set of squares in its second argument's set attacked by a piece in its first argument. Thus,
attack (k _)is the set of empty squares attacked by the black King, that is, the empty squares in the King's field. Therefore
attack (A attack (k _))is the set of empty squares in the Black King's field that are attacked by a white piece. To see this, note that the first "attack" filter has two arguments:
attack (k _)
Ais the white pieces (technically, the squares in the current position on which a white piece lies). The second argument,
attack (k _), we have just seen represents the empty squares in the Black King's field.
combining square setsAn
orfilter is a square set if its two arguments are. Thus,
R or na3is the set of squares in the current position on which lie either a white Rook or a black knight on a3. but
R or checkis not a square set. If you try and use it as one, like
attack (R or check K)an error will result. But
attack (R or na3 K)would be legal. It would be associated with the square on which the K lies exactly if the K is attacked with by a White R or by a black knight on a3.
Using sets as filtersIf a filter is a set-filter, then it matches a position exactly when the set associated with the filter for that position is nonempty. This agrees with how we think of things generally. For example, the filter R matches a position if the position has a white rook in it; which is exactly when the set of squares on which a white rook lies is nonempty.
Filters with a range are never setsSome filters are sets normally, but not if they take a range. For example
attack (A p)is a filter that is true if a white piece is attacking a black pawn, and is associated with the set of squares on which an attacked black pawn lies. But
attack 1 (A p)is a filter that is true if exactly one white piece is attacking exactly one black pawn. This is not a set filter.