Abstract: Techniques are described herein for using operational transforms to perform operations on parallel copies of a document model. A method includes: determining that a first operation is to be performed on a second parallel copy; and in response: determining that a revision of a first parallel copy matches a revision of the second parallel copy; and in response: performing the first operation on the second parallel copy to obtain a calculation result including a first list of commands; applying the first list of commands to the second parallel copy; performing an operational transform on at least one command in the first list of commands based on queued user edits to the first parallel copy, the queued user edits including a second list of commands, to obtain a transformed list of commands; and applying the transformed list of commands to the first parallel copy.

Abstract: Techniques are described herein for using operational transforms to perform operations on parallel copies of a document model. A method includes: determining that a first operation is to be performed on a second parallel copy; and in response: determining that a revision of a first parallel copy matches a revision of the second parallel copy; and in response: performing the first operation on the second parallel copy to obtain a calculation result including a first list of commands; applying the first list of commands to the second parallel copy; performing an operational transform on at least one command in the first list of commands based on queued user edits to the first parallel copy, the queued user edits including a second list of commands, to obtain a transformed list of commands; and applying the transformed list of commands to the first parallel copy.

Abstract: Mutations representing spreadsheet edit operations are received at a server from client computers of collaborators and also at a collaborator's client computer from other collaborators and the server. Different mutations may conflict, i.e., provide contradictory instructions on how a spreadsheet is to be edited. Techniques for representing sort operations, cut-and-paste operations, and operations to change cell properties as mutations, and operational transform techniques that can be used to resolve conflicts between such mutations, are disclosed herein. Further disclosed herein are techniques for identifying and processing computationally intensive types of mutations in a calculation thread which operates asynchronously with respect to a UI thread at a collaborator's client computer. The processing may include performing an operational transform on results of the calculation thread based on results obtained in the UI thread.