# flipvertical

`flipvertical` is a transform filter corresponding to the following 2 basic transforms.
• id, the identity
• reflectv: reflection about the vertical bisector.

`flipvertical` is normally called with a single argument filter, F:

`      flipvertical F`

`flipvertical` also accepts an optional `count` parameter. `flipvertical 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 reflectv we get the new filter `{Kh1 ka8}`. The filters that results from transforming `{Ka1 kh8}` by all the elements of `flipvertical`, which is to say the identity and reflection about the vertical bisector, are:

```  {Ka1 kh8}
{Kh1 ka8}```

The filter `flipvertical {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 `h1` and the black king is on the opposite corner. (This can also be done, more efficiently, via `k==diagonal 7 K[a1,h1]` )

If F is a set filter then so is

`flipvertical 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,

`flipvertical a1` is the set `[a1,h1]`.

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

`flipvertical 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

`flipvertical count find {Qa1 qh8}`

is equal to 0 if neither `{Qa1 qh8}` nor `{Qh1 qa8}` 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 `flipvertical` filter also modifies directions parameters and filters. Thus,

`flipvertical ray right (R K)`

will match if and only if

`ray horizontal (R K)`

matches.