The ray filter

The ray filter is used to find patterns of pieces that are arranged along a straight line.

A ray filter consists of the keyword ray followed by an optional directions followed by a list of set filters enclosed in parentheses: 

ray (△ ▲ )
ray up (△ ▲ ♙)
ray vertical (△ △ △ ▲ ♚)

Note: most of the time in CQL, the simpler → is all that is needed instead of ray.

A ray on the chessboard is the set of squares along a straight line from a given start point along one of the 8 basic directions .

For example, there is an up ray from the start point e2. That ray has seven squares, e2-8:

ray from e2 to e8

Each ray orders the squares on that ray. The ordering is determined by the direction of the ray. If squares s and t are on the ray, then s is earlier than t if t can be reached from s by moving along the ray's basic direction.

For example, in the up ray starting on e2, the square e3 is earlier than e7. But in a down ray starting on e8, the square e7 is earlier than e2.

The basic directions of a ray filter are the basic directions contained in the set of directions indicated by its direction parameter (recall that some directions represent a set of basic directions: vertical represents the set containing up and down for example. If there is no direction parameter to the ray filter, the direction parameter is taken to be anydirection, all the 8 basic directions.

Let R be the following ray filter: 

  ray dirs (s1 s2 ... sn)
where dirs indicates a set of basic directions and each si is a set filter.

A ray matches the ray filter R if there is a sequence S of n distinct squares on the ray such that

  • The i'th square of S is a member of the set represented by the set filter si
  • The direction of the ray is a member of the set of basic directions indicated by dirs
  • There are no pieces between two consecutive squares in S

R is also a set filter representing the set of squares s that terminate some sequence S above.

Examples of rays

This filter is true whenever a black knight is pinned by a white rook: 
  ray orthogonal (♖ ♞ ♚)
  ≡
  ♖→♞→♚

To match a position where some piece is pinned by a rook of either color, use: 

  ⬓ray orthogonal (R a k)
  ≡
  ⬓♖→▲→♚

Suppose the current position is the position after 

 
1. e4 e5
2. ♘f3 ♘c6

some rays

One ray that would match the position is 

  ray diagonal (c6 e4 f3)

That is because starting at c6 the ray moves diagonally, skipping over empty squares (one empty square in this case at d5 and the reaches e4, and then, skipping over zero empty squares, reaches f3.

If this position were the current position, then ♞ represents the squares [c6,g8]; ♙ represents the squares [a2,b2,c2,d2,e4,f2,g2,h2] and ♘ represents the squares [f3,b1]. Thus, the pictured ray would also match the filter 

  ray diagonal (♞ ♙ ♘)

Likewise, the diagram depicts a matching 

  ray (e1 e4 e5 e8)
Therefore, the following two filters would also match the diagrammed position: 
ray up (♔ ♙ ♟ ♚)
ray up (♔ □ ♙ ♟ □ ♚)

Some other matching rays in the position: 

ray right (♜ ♝ ♛ ♚)
ray northeast (♖ ♙ ♟ ♟ ♜)
ray diagonal (♗ ♙ h6)
ray (♕ c2)
ray orthogonal (♔ ♙)
However, the following ray filter would not match the position: 
  ray (♔ ♟)

This is because there is a white pawn between the king at e1 and the best target of such a ray, the black pawn at e5.

Examples

The ray filter is used in wurzburg-plachutta.cql