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system
does modifying an order cancel the old one and submit a new one
user
limit books are managed by exchanges. if an order is not immediately filled, it is sent to the book.  from there, orders are generally executed on price-time-priority.  the one major exception is the precedence hide-not-slide orders have over earlier placed visible slidden limit orders since unslidden orders are treated like a modification/cancellation. to an exchange, a modification is the same as a cancellation since it charges no fees for placing or canceling orders, only for trades.  the timestamp is reset, and price-time-priority is applied in the same way, so if a modified order isn't immediately filled, it is sent back to the book to be filled in order of price-time-priority.
assistant