WIP: feat: mechanization of "Interval Tree Clocks" - #13
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This PR introduces a simplified version of "Interval Tree Clocks", described by Almeida et al. in their similarly named paper. Note: we just introduce the tree-based definitions, and prove they have the desired properties directly, without defining the denotation of such trees into actual intervals/sets. We also simplify the model a lot, by removing arbitrary events, and instead saying that a merge also counts as an event. By doing so, we can replace the event-tree by a single natural number, making it much simpler to reason about. We do use the id-tree exactly as defined in the paper, but since we eliminated the tree structure from the event component, we had to come up with a novel definition of the happens-before relation. This gives us a clock with a fork and join operations. This PR also proves that the arguments to these operations always happen before their results. Desired properties around independence are stated, but not yet proven. WIP because I had to last-minute tweak the happens-before relation, and should still check that the new definition (a) actually is the correct one, and (b) is consistent with the documentation.
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Unfortunately, the simplifications made the happens-before relation non-transitive, which disqualifies it. |
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This PR introduces a simplified version of "Interval Tree Clocks", described by Almeida et al. in their similarly named paper.
Note: we just introduce the tree-based definitions, and prove they have the desired properties directly, without defining the denotation of such trees into actual intervals/sets.
We also simplify the model a lot, by removing arbitrary events, and instead saying that a merge also counts as an event. By doing so, we can replace the event-tree by a single natural number, making it much simpler to reason about. We do use the id-tree exactly as defined in the paper, but since we eliminated the tree structure from the event component, we had to come up with a novel definition of the happens-before relation.
This gives us a clock with a fork and join operations. This PR also proves that the arguments to these operations always happen before their results. Desired properties around independence are stated, but not yet proven.
WIP because I had to last-minute tweak the happens-before relation, and should still check that the new definition (a) actually is the correct one, and (b) is consistent with the documentation.