Overview of ←

The ← filter (ascii <-) is the dual of → . As with → we can divide usages of ← into binary, ternary, and n-ary forms.

A ← filter is true exactly when the → filter formed by reversing all the arrows and the order of the constituent filters is true: 

      y←x
is true exactly when 
      y→x
is true. 

      z←y←x
is true exactly when 
      x→y→z
is true.

value returned by ←

The reason to use ← rather than → is that the value returned by the filters is different.

The value returned by y→x is all squares in y that are attacked by x.

In general, if Z is a set filter, then the value of a chain of ← filters is loosely speaking, all the squares in the first filter in the chain that make the filter true.

←, binary case

The filter 
    x←y
is true exactly when 
    y→x
is true.

However, the value of 

    y←x
is the set of squares in y that are attacked by a piece in x.

For example, if the current position is the start position, then 

    ♙←♘
    ≡
    [e2,d2]

← chains

z←y←z
matches a position if and only if 
x→y→z
matches the position.

The value returned by 

z←y←z
is the set of squares Z in z such that 
Z←y←x
matches the position.

Likewise, 

x1→x2→x3→...→xn
matches a position if and only if 
      xn←xn-1←...←x1
matches the position.

As before, the value of 

          xn←xn-1←...←x1
is the set of X in xn such that 
          X←xn-1←...←x1

Examples

The black king's field, which is the set of squares attacked by the black king, is 
      ▦←♚

Thus, to check that a white pawn is guarding an empty square in the black king's field, use: 

      ♙→(□←♚)

To check that the maximum 27 squares are attacked by a white queen, use 

      ▦←♕==27
(As in maxqueenattack.cql).