# 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:(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:

(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:

(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`

:

(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):

(found from CQL file: turton.cql)

Now white moves `U`

to the critical square `C`

, completing the reorientation of `T`

and `U`

:

(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`

:

(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∪Utells 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→fromThis 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 " Cinserts 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.