# turton.cql

The CQL file turton.cql shows how to find examples of the Turton theme. The Turton theme is a beautiful problem theme that we illustrate here with an endgame study by one of the CQL developers:
Costeff 2015, after 4...Rf4
(found from CQL file: turton.cql)

There are two thematic pieces to a Turton, which we call `T` and `U`. These must be line pieces, a `♕`, `♖` or `♗` that can slide along the same direction (so that `♖♗`) are disallowed. The idea of the Turton is that white wants to double `T` and `U` so that `T` will support `U` after a move by `U`. In order to arrange this doubling, `T` passes over a critical square `C` and then allows `U` to move to `C`. Had `U` just moved initially to `C`, then `T` would move forward supported by `U`. The idea of the Turton is that `T` and `U` switch orientations so that `U` can move forward.

In the diagramed position `T` is the `♕e3`; `U` is the `♖a2`; and `C` is e2.

White would like to check black on `e8` with `T` or `U`, supported by the other. The immediate `4.♖e2` fails:

after 4. Re2? (variation)
(found from CQL file: turton.cql)

due to `4...♜×f7`, when `5.♕e8+` fails due to `5...♜f8`.

Thus, White can only win by switching the orientation of the `♕/♖` pair. White does this in a surprising way: `4.♕e7! ♛d1` reaching this position:

Costeff 2015, after 4...Qd1+
(found from CQL file: turton.cql)

Now white begins the main Turton theme with the critical move by `T`: `5.♕e1`, crossing the critical square `C`:

after 5.Qe1
(found from CQL file: turton.cql)

Suprisingly, `5.♕×e1 6.♔×g2` wins here for white, so black tries to retreat with `5.♕d8` (stopping the back rank mate):

after 5....Qd8
(found from CQL file: turton.cql)

Now white moves `U` to the critical square `C`, completing the reorientation of `T` and `U`:

after 6. Re2
(found from CQL file: turton.cql)

Black tries his first defense with `♖×f6` but this now fails to `7.♖e8+` because `U` (the `♖` on `e8` is supported by `T`, the `♕e1`:

after 7. Re8+ 1-0
(found from CQL file: turton.cql)

# turton.cql line-by-line

The first line simply guesses values for `T`, `U` and `C`. `T` will be a piece variable that is one of `♕♖♗`:
`    ◭T∊♕♖♗`
`T` is a piece variable (like the piece variable in explain-likeinterference.cql) whose value is the square on which the selected piece lies. This represents the supporting piece in the Turton theme, one of `♕♖♗`. `U` is another piece variable, the supported piece. The `∩~T` insures that `U` is a distinct piece from `T`, since `~T` are all the squares other than the one `T` is on. `C` is the critical square, an ordinary square variable. It can range over all the empty squares initially attacked by `U`, that is, `□←U`.

Once candidate assignments for `T`, `U`, and `C` have been determined, the main work of the CQL file begins. The

`⊢T∪U`
tells the `⊢` only to consider moves by the thematic pieces `T` and `U`.

The first constituent of the path indicates that the thematic `T` first moves to an empty square:

`T――□`

The next constituent is a filter constituent

`T→C→from`
This filter is evaluated in the position after `T` makes its first move (to an empty square, `□`). The value of from is the square from which `T` moved. The chained indicates that that the three squares `T`, `C` and `from` are in a line, with the critical square `C` being attacked by `T`. Since `T` is as line piece, this means that `T` has crossed over the square `C` as if moved from `from` to its current square.

The comment

`///"T crosses critical square " C`
inserts the specified comment into the PGN file as a comment to the critical move. Note that the `C` in the comment is replaced by the actual square's name.

The next move of the theme is

`U――C`
This indicates that `U` moves to the critical square. There can of course be any number of moves by non-thematic piece in between these first two thematic moves. Finally, `U` moves to a square where it is supported by `T` through the now-empty critical square `C`:
`U―― T→C→U`

# summary

Using piece variables and `――◎` can allow a concise description of the key ideas of a Turton theme, including the motion of thematic pieces and the concept of a critical move that crosses a critical square.