fliphorizontal

fliphorizontal is a transform filter corresponding to the following 2 basic transforms.
• id, the identity
• reflecth: reflection about the horizontal bisector.

fliphorizontal is normally called with a single argument filter, F:

fliphorizontal F

fliphorizontal also accepts an optional count parameter. fliphorizontal F matches the current position if any transformation of F by one of the 2 basic transforms above matches the current position. These two transforms are examples of dihedral transforms.

For example, suppose F is the filter {Ka1 kh8}, matching a position in which the white king is on a1 and the black king is on h8. If we transform this filter by reflecth we get the new filter {Ka8 kh1}. The filters that results from transforming {Ka1 kh8} by all the elements of fliphorizontal, which is to say the identity and reflection about the horizontal bisector, are:

{Ka1 kh8}
{Ka8 kh1}

The filter fliphorizontal {Ka1 kh8} will thus match a position if either of these two filters match the position, that is, if the white king is on a1 or a8 and the black king is on the opposite corner. (This can also be done, more efficiently, via k==diagonal 7 K[a1,a8] )

If F is a set filter then so is

fliphorizontal F

in which case its value is the union of the values of each of the sets represented by each transformed version of F.

For example,

fliphorizontal a1 is the set [a1,a8].

If F is a numeric filter then so is fliphorizontal F in which case its value is the maximum of the values of F and the value of the reflection of F about the horizontal bisector.

fliphorizontal count F

is a numeric filter whose value is the number of distinct matching transformed versions of F. For example, if the current position is the initial position, then

fliphorizontal count find {Qa1 qh8}

is equal to 0 if neither {Qa1 qh8} nor {Qa8 qh1} occur in the game; is equal to 1 if exactly one of these configurations does; and is equal to 2 if both of them do.

The fliphorizontal filter also modifies directions parameters and filters. Thus,

fliphorizontal ray up (R K)

will match if and only if

ray vertical (R K)

matches.