Editing Pure mate (section)

==Exceptions for double check and pins==
Some authors allow exceptional cases involving double check and pins to count as pure mates, even if they violate the basic concept that each square of the field (and the king's square itself) is covered exactly once. Such exceptions are allowed if the existence of a double check or a pin is {{em|necessary}} in order for the position to be a checkmate, preventing the mated party from responding to the check, which they might otherwise have done.  

In chess composition, the aesthetic concept which allows for this expanded definition of pure mate is called ''economy of force''.{{sfn|Horton|p=56}}{{sfn|Hooper & Whyld|p=119}} Economy of force refers to the idea that a chess composition is simpler and more beautiful when it uses minimal material to maximal effect, e.g. in a checkmate or some particular tactic. Ideally, in order to avoid redundancy, no more than one unit should attack a given square. But if the minimum force necessary in order to ensure checkmate requires a double check or a pin, then the resulting position may be regarded as a pure mate.

In the first diagrammed position, Black has been mated by a double check.<ref name="Beasley" /> Every square of the king's field is attacked, guarded, or blocked exactly once. However, the king's square itself is attacked twice. In a double check, it is impossible for a defender to block or capture both attackers simultaneously. Therefore the king must move, and in the given position, it cannot. If the position were not a double check, then the black queen would be able to deal with either check, either by interposing between the rook and the king at e5, between the bishop and the king at e4, or else by capturing the rook at f5. Double check prevents the queen from moving at all. The fact that the position is a double check is necessary in order for it to be a checkmate, and therefore some authors allow it as a pure mate.{{efn|Other authors may allow such a position to count as a pure mate, for the simple reason that they do not consider the king's square itself in their definition.<ref name="mayhem" />}}

In the second diagrammed position, Black has been mated by the knight at e3.<ref name="Beasley" /> Every square in the king's field and the king's square itself are each covered exactly once, with one exception. The black king cannot move to e4 for two reasons: the square is occupied by a friendly rook, but even if it weren't, the square is also attacked by the white bishop, which pins the rook to its king. However, the fact that the rook is pinned is necessary in order for the position to be a checkmate. If the rook were not pinned, it would be able to deal with the check by capturing the knight at e3. Both of these examples satisfy Hooper and Whyld's expanded definition of pure mate.{{sfn|Hooper & Whyld|pp=326-327}}

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| A position involving a double check may be regarded as pure mate, if the double check was necessary to ensure checkmate.
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| A position involving a friendly piece pinned in the mated king's field may be regarded as pure mate, if the pin is necessary to ensure checkmate.
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===Non-examples===
In the first non-example shown, White can play 1.Re8#. If this move is played, Black will be mated by double check. The position might be a pure mate, except that a8 is attacked twice, by both the white rook and bishop. Even if the resulting position were not a double check, Black has no way of addressing either or both attacks. In other words, it was not necessary to play the double check in order to prevent Black from capturing an attacker or interposing into a line of attack. Therefore, the double check would represent additional and unnecessary attacking force, above the minimum required for mate and contrary to the concept of economy of force. Thus, the position following 1.Re8# fails to satisfy Hooper and Whyld's definition of a pure mate.{{sfn|Hooper & Whyld|pp=326-327}} White could instead play 1.Qc8#, a genuine pure mate delivered by an unassisted queen.

In the second non-example, White can play 1.Bd5#. If this move is played, Black will be mated in a position involving a pinned piece in the king's field. The position might be a pure mate, except that a7 is both occupied by a friendly pawn and also attacked by the white queen. The pin is unnecessary to the checkmate, because even if the pawn were not pinned, it would still not be able to capture the attacking bishop or to interpose in the bishop's line of attack. If, after 1.Bd5#, the white queen were removed from the board, the position would still be a checkmate. Therefore, the pin represents additional and unnecessary attacking force, above the minimum required for mate and contrary to the concept of economy of force. Thus, the position fails to satisfy Hooper and Whyld's definition of a pure mate.{{sfn|Hooper & Whyld|pp=326-327}} White could instead play 1.Qd5#, simultaneously unpinning the black pawn and delivering a genuine pure mate.

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| The position following 1.Re8# is not accepted as pure mate, because the double check involves superfluous attacking force. Instead, 1.Qc8# would be a pure mate.
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| Non-example 2 
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| The position following 1.Bd5# is not accepted as pure mate, because there is no need to keep the pawn pinned to a7 in order to checkmate.  Instead, 1.Qd5# unpins the pawn and delivers a pure mate.
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