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"Yes there is. A half-move is a move made by one player; it's half a ply where a ply is two half-moves made by each player. "
You're playing with words. When one refers to a move, it is usually an individual piece being placed on a different location on the chess board. It is usually not thought of as the completion of both white and black turns. Thus, you are trying to use a definition which is in discord with common language, creating confusion. A better way to say this would be: "White to play and mate!"
Also, unless the players agree to a conclusion, there is no win in 0.5 moves. There is only a mate in two moves in normal language and 1.5 moves by your definition of a move.