The terms "fullmove" and "halfmove" (sometimes used with spaces, i.e. "full move", sometimes hyphenated i.e. "half-move", sometimes capitalised i.e. "Half-move", "Fullmove", sometimes all used interchangeably in the same document), as well as the term "ply", are often used in chess programming.
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"Plies" is the plural of "ply".
A halfmove is a piece movement of *one* side. It is usually what I mean in this document if I say "move" without qualification.
Ply is a synonym for halfmove, but ply is used more frequently when the term is part of an adjective phrase ("6 ply search", "search" is the noun, and "6 ply" modifies it).
A fullmove is pair of consecutive halfmoves, usually restricted to consecutive pairs of halfmoves which start with a halfmove by white and end with a halfmove by black.