xray

The xray filter is a sort of generalized pin.

In a pin, the pinning piece would attack a target piece except for the presence of a pinned piece. But in a normal pin the colors of the pinning piece and the pinned piece are different.

In an xray, we allow any configuration of pieces in a line, in which the last piece in the line would be attacked by the first piece in the line except for the presence of the other pieces in th eline.

Examples of xrays are:

  xray (R a k)
  xray (Q A K)

The first filter xray (R a k) matches a position where a black piece (the a) is pinned by a white rook (R) to the black king (k):

xray(b5 d5 g5)

It is an xray because without the bishop on d5, the R would attack the k.

However, this filter would not match the following position:

not xray(b3 d5 f7)

because even without the bd5 the R does not attack the k.

The second filter xray (Q A K) matches a position where there is a single white piece (A) between a white queen (Q) and the white king (K), e.g.:

xray(b3 d5 f7)

Specification

More formally, the xray filter takes any number of set filter arguments enclosed in parentheses. For simplicity we discuss the case of 3 arguments:

  xray (x y z)

Here x, y, and z are set filters. Suppose in the current position these set filters correspond to sets of squares X, Y, and Z respectively.

Then the above xray filter matches a position if there are distinct squares sx, sy, and sz in X, Y, and Z respectively such that

• sx contains a line piece (rook, bishop or queen)
• The piece on sx attacks sy
• If the square sy were empty, then sx would attack sz
• If the square sy were occupied by a piece, then sx would not attack sz

This is extended to more than three arguments exactly as in the case of ray. In fact, xray can be defined in terms of ray:

Any xray of the form

  xray (x other_args)

where other_args is a sequence of set filters, is equivalent to:

  ray orthogonal ({x&[RrQq]} other_args)
  | ray diagonal ({x&[BbQq]} other_args)

Examples

The xray filter is used in bristol-universal.cql, idealmate.cql, modelmate.cql, indian.cql, turton.cql and puremate.cql.

An unusual 4 argument xray filter is used in indian.cql, where if finds the following study:

Costeff 1996 after 1...e2
(found from CQL file: indian.cql)

In the diagrammed position, White has to be worried both about stalemating black if the pawns on e2, a7, e7 disappear or run out of moves; and of course about the ng1 moving and freeing the pawns ph2,pg2. White has two reasonable moves: 2.Ra1 and 2.Rb1. It turns out that only 2.Rb1 wins, as the position after 2.Rb1 a6 3.Ra1 is zugzwang: black to move loses, white to move draws. If White had played immediately 2.Ra1? then black responds 2...a6! reaching the zugzang position with white to move.

One reason for this is an Indian theme. White promotes the Pd5 to a bishop and interposes it to b1, preventing stalemate:

xray(a1 b1 g1 h1) from Costeff 1996, after 12.Bb1
(found from CQL file: indian.cql)

One of the elements of the Indian theme is that White moves to a critical square (here the move 12.Bb1) in order to prevent stalemate. The CQL code in indian.cql is somewhat convoluted, but for our purposes the key filter is:

  xray (rear critical x k)

The goal of this filter is to express the concept that the piece on x would be pinned if not for the piece on critical. In the diagrammed position, rear has value a1; critical has value b1; x has value g1; and the k is on h1. The rook on a1 would attack the kh1 but for the pieces on b1 and g1. Equivalently, the ng1 is pinned but for the Bb1.

(This study actually expresses a double Indian, because at move 10 the bishop had moved to d1, also preventing stalemate, which explains the apparent duplicate comments in the PGN file).