purestalemate

The purestalemate filter is true in a position if the position is a pure stalemate. A pure stalemate, loosely speaking, is one in which there is no unnecessary attack by the mating side on a square adjacent to the mated King.

More formally, a black-to-move position is a pure stalemate if each of the following conditions holds:

• each empty square adjacent to the black king is attacked exactly once by a white piece;
• each white piece adjacent to the black king is attacked exactly once by a white piece;
• each unpinned black piece adjacent to the black king is not attacked by a white piece; and
• each pinned black piece adjacent to the black king is not attacked by a white piece.

A white-to-move pure stalemate is defined similarly.

Participants: the value of the purestalemate filter

If the current position is a pure stalemate, the value of the puremate filter is the set of squares on which there is a participating piece. If the current position is not a pure mate, the value returned is the empty set.

If the current position is a pure stalemate of the black King, the participating white pieces are each white piece that either:

1. is pinned;
2. is pinning a black piece
3. is attacking a square adjacent to the black king.

Every black piece is considered to be a participating piece when black is in stalemate.

If white is in stalemate, the definitions above are modified accordingly.

modelstalemate

The modelstalemate filter is true if the current position is a model stalemate: a pure stalemate in which each non-King, non-pawn piece of the stalemating side participates. Thus, modelstalemate is true in position whenever

  ⬓{
   btm purestalemate
  ♖♘♗♕ in purestalemate}

(Note that the first purestalemate in the CQL code above cannot be omitted, because otherwise any black-to-move position that is not a pure stalemate would match if the only white pieces were kings and pawns.)

The value of the modelstalemate filter, like the purestalemate filter, is the set of participants in the model stalemate (or the empty set if there is no model stalemate).

idealstalemate

The idealmate filter is true if the current position is an ideal stalemate: a pure stalemate in which each piece participates. The idealstalemate filter is equivalent to:

  ◭==purestalemate