∪ filter

The ∪ filter has the syntax:

  left ∪ right

where left and right are each filters. The left and right arguments must each be set filters.

The ∪ filter is a set filter whose value is the union of the sets of squares represented by its arguments.

For example,

  pin ∪
  {♖→♚}

is the set of squares on which there is either a pinned piece or there a white rook attacking the black king. The left argument to the ∪ filter is pin whose value is the set of squares on which there is a pinned piece. The right argument to the ∪ filter is {♖→♚} , whose value is the set of squares on which there is a white rook which attacks the black king. The value of the ∪ filter is the union of these two sets.

Examples

The ∪ filter is used throughout the examples.